<Page>

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-CSR

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                         MANAGEMENT INVESTMENT COMPANIES

Investment Company Act file number: 811-03326

Morgan Stanley U.S. Government Money Market Trust
               (Exact name of registrant as specified in charter)

1221 Avenue of the Americas, New York, New York 10020
              (Address of principal executive offices)                (Zip code)

Ronald E. Robison
1221 Avenue of the Americas, New York, New York 10020
                                      (Name and address of agent for service)

Registrant's telephone number, including area code: 212-762-4000

Date of fiscal year end: January 31, 2006

Date of reporting period: January 31, 2006

Item 1 -  Report to Shareholders
<Page>

WELCOME, SHAREHOLDER:

IN THIS REPORT, YOU'LL LEARN ABOUT HOW YOUR INVESTMENT IN MORGAN STANLEY U.S.
GOVERNMENT MONEY MARKET TRUST PERFORMED DURING THE ANNUAL PERIOD. WE WILL
PROVIDE AN OVERVIEW OF THE MARKET CONDITIONS, AND DISCUSS SOME OF THE FACTORS
THAT AFFECTED PERFORMANCE DURING THE REPORTING PERIOD. IN ADDITION, THIS REPORT
INCLUDES THE FUND'S FINANCIAL STATEMENTS AND A LIST OF FUND INVESTMENTS.

THIS MATERIAL MUST BE PRECEDED OR ACCOMPANIED BY A PROSPECTUS FOR THE FUND BEING
OFFERED.

MARKET FORECASTS PROVIDED IN THIS REPORT MAY NOT NECESSARILY COME TO PASS. THERE
IS NO ASSURANCE THAT A MUTUAL FUND WILL ACHIEVE ITS INVESTMENT OBJECTIVE. AN
INVESTMENT IN A MONEY MARKET FUND IS NOT INSURED OR GUARANTEED BY THE FEDERAL
DEPOSIT INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY. ALTHOUGH THE FUND
SEEKS TO PRESERVE THE VALUE OF AN INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE
TO LOSE MONEY BY INVESTING IN THE FUND. PLEASE SEE THE PROSPECTUS FOR MORE
COMPLETE INFORMATION ON INVESTMENT RISKS.

<Page>

FUND REPORT
For the year ended January 31, 2006

MARKET CONDITIONS

During the 12-month period ended January 31, 2006, the Federal Open Market
Committee (the "Fed") continued its pattern of raising short-term rates which
began in June of 2004. Through 14 steps of 25 basis points each -- including
nine during the 12 months covered by this report -- the Fed increased its target
rate for federal funds from 1.00 percent to 4.50 percent.

Short-term rates rose alongside the federal funds rate, providing increased
return opportunities for investors in money market funds.

PERFORMANCE ANALYSIS

As of January 31, 2006, Morgan Stanley U.S. Government Money Market Trust had
net assets in excess of $937 million and an average portfolio maturity of 36
days. For the 12-month period ended January 31, 2006, the Fund returned 2.71
percent. For the seven-day period ended January 31, 2006, the Fund provided an
effective annualized yield of 3.70 percent and a current annualized yield of
3.63 percent, while its 30-day moving average annualized yield for January was
3.62 percent. PAST PERFORMANCE IS NO GUARANTEE OF FUTURE RESULTS.

Our strategy in managing the Fund remained consistent with our long-term focus
on preservation of capital and liquidity. We adhered to a conservative approach
in managing the Fund, emphasizing high-quality money market obligations. We
avoided the use of derivatives or structured notes that might fluctuate
excessively with changing interest rates. We also took advantage of the rising
yields available on the money market securities. As short-term interest rates
climbed, we reinvested the proceeds of maturing short-term holdings into
higher-yielding securities.

PORTFOLIO COMPOSITION

<Table>
                                            
U.S. Government Agencies                       81.3%
Repurchase Agreements                          18.1
U.S. Treasury Bill                              0.6
</Table>

MATURITY SCHEDULE

<Table>
                                            
  1 - 30 Days                                  66.6%
 31 - 60 Days                                  13.8
 61 - 90 Days                                   8.7
 91 - 120 Days                                  0.9
121 + Days                                     10.0
</Table>

DATA AS OF JANUARY 31, 2006. SUBJECT TO CHANGE DAILY. ALL PERCENTAGES FOR
PORTFOLIO COMPOSITION AND MATURITY SCHEDULE ARE AS A PERCENTAGE OF TOTAL
INVESTMENTS.

                                        2
<Page>

INVESTMENT STRATEGY

THE FUND WILL INVEST IN HIGH QUALITY, SHORT-TERM U.S. GOVERNMENT SECURITIES. THE
FUND'S "INVESTMENT ADVISER," MORGAN STANLEY INVESTMENT ADVISORS INC., SEEKS TO
MAINTAIN THE FUND'S SHARE PRICE AT $1.00. THE SHARE PRICE REMAINING STABLE AT
$1.00 MEANS THAT THE FUND WOULD PRESERVE THE PRINCIPAL VALUE OF YOUR INVESTMENT.

AN INVESTMENT IN THE FUND IS NOT INSURED OR GUARANTEED BY THE FEDERAL DEPOSIT
INSURANCE CORPORATION OR ANY OTHER GOVERNMENT AGENCY. ALTHOUGH THE FUND SEEKS TO
PRESERVE THE VALUE OF YOUR INVESTMENT AT $1.00 PER SHARE, IT IS POSSIBLE TO LOSE
MONEY BY INVESTING IN THE FUND.

FOR MORE INFORMATION ABOUT PORTFOLIO HOLDINGS

EACH MORGAN STANLEY FUND PROVIDES A COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS IN
ITS SEMIANNUAL AND ANNUAL REPORTS WITHIN 60 DAYS OF THE END OF THE FUND'S SECOND
AND FOURTH FISCAL QUARTERS BY FILING THE SCHEDULE ELECTRONICALLY WITH THE
SECURITIES AND EXCHANGE COMMISSION (SEC). THE SEMIANNUAL REPORTS ARE FILED ON
FORM N-CSRS AND THE ANNUAL REPORTS ARE FILED ON FORM N-CSR. MORGAN STANLEY ALSO
DELIVERS THE SEMIANNUAL AND ANNUAL REPORTS TO FUND SHAREHOLDERS AND MAKES THESE
REPORTS AVAILABLE ON ITS PUBLIC WEB SITE, www.morganstanley.com. EACH MORGAN
STANLEY FUND ALSO FILES A COMPLETE SCHEDULE OF PORTFOLIO HOLDINGS WITH THE SEC
FOR THE FUND'S FIRST AND THIRD FISCAL QUARTERS ON FORM N-Q. MORGAN STANLEY DOES
NOT DELIVER THE REPORTS FOR THE FIRST AND THIRD FISCAL QUARTERS TO SHAREHOLDERS,
NOR ARE THE REPORTS POSTED TO THE MORGAN STANLEY PUBLIC WEB SITE. YOU MAY,
HOWEVER, OBTAIN THE FORM N-Q FILINGS (AS WELL AS THE FORM N-CSR AND N-CSRS
FILINGS) BY ACCESSING THE SEC'S WEB SITE, http://www.sec.gov. YOU MAY ALSO
REVIEW AND COPY THEM AT THE SEC'S PUBLIC REFERENCE ROOM IN WASHINGTON, DC.
INFORMATION ON THE OPERATION OF THE SEC'S PUBLIC REFERENCE ROOM MAY BE OBTAINED
BY CALLING THE SEC AT (800) SEC-0330. YOU CAN ALSO REQUEST COPIES OF THESE
MATERIALS, UPON PAYMENT OF A DUPLICATING FEE, BY ELECTRONIC REQUEST AT THE SEC'S
E-MAIL ADDRESS (publicinfo@sec.gov) OR BY WRITING THE PUBLIC REFERENCE SECTION
OF THE SEC, WASHINGTON, DC 20549-0102.

HOUSEHOLDING NOTICE

TO REDUCE PRINTING AND MAILING COSTS, THE FUND ATTEMPTS TO ELIMINATE DUPLICATE
MAILINGS TO THE SAME ADDRESS. THE FUND DELIVERS A SINGLE COPY OF CERTAIN
SHAREHOLDER DOCUMENTS, INCLUDING SHAREHOLDER REPORTS, PROSPECTUSES AND PROXY
MATERIALS, TO INVESTORS WITH THE SAME LAST NAME WHO RESIDE AT THE SAME ADDRESS.
YOUR PARTICIPATION IN THIS PROGRAM WILL CONTINUE FOR AN UNLIMITED PERIOD OF TIME
UNLESS YOU INSTRUCT US OTHERWISE. YOU CAN REQUEST MULTIPLE COPIES OF THESE
DOCUMENTS BY CALLING (800) 350-6414, 8:00 A.M. TO 8:00 P.M., ET. ONCE OUR
CUSTOMER SERVICE CENTER HAS RECEIVED YOUR INSTRUCTIONS, WE WILL BEGIN SENDING
INDIVIDUAL COPIES FOR EACH ACCOUNT WITHIN 30 DAYS.

                                        3
<Page>

EXPENSE EXAMPLE

As a shareholder of the Fund, you incur ongoing costs, including advisory fees;
distribution and service (12b-1) fees; and other Fund expenses. This example is
intended to help you understand your ongoing costs (in dollars) of investing in
the Fund and to compare these costs with the ongoing costs of investing in other
mutual funds.

The example is based on an investment of $1,000 invested at the beginning of the
period and held for the entire period 08/01/05 - 01/31/06.

ACTUAL EXPENSES

The first line of the table below provides information about actual account
values and actual expenses. You may use the information in this line, together
with the amount you invested, to estimate the expenses that you paid over the
period. Simply divide your account value by $1,000 (for example, an $8,600
account value divided by $1,000 = 8.6), then multiply the result by the number
in the first line under the heading entitled "Expenses Paid During Period" to
estimate the expenses you paid on your account during this period.

HYPOTHETICAL EXAMPLE FOR COMPARISON PURPOSES

The second line of the table below provides information about hypothetical
expenses based on the Fund's actual expense ratio and an assumed rate of return
of 5% per year before expenses, which is not the Fund's actual return. The
hypothetical account values and expenses may not be used to estimate the actual
ending account balance or expenses you paid for the period. You may use this
information to compare the ongoing cost of investing in the Fund and other
funds. To do so, compare this 5% hypothetical example with the 5% hypothetical
examples that appear in the shareholder reports of the other funds.

Please note that the expenses shown in the table are meant to highlight your
ongoing costs only. Therefore, the second line of the table is useful in
comparing ongoing costs, and will not help you determine the relative total cost
of owning different funds that have transactional costs, such as sales charges
(loads), and redemption fees, or exchange fees.

<Table>
<Caption>
                                                     BEGINNING         ENDING         EXPENSES PAID
                                                   ACCOUNT VALUE    ACCOUNT VALUE    DURING PERIOD *
                                                   -------------    -------------    ---------------
                                                                                       08/01/05 -
                                                      08/01/05         01/31/06         01/31/06
                                                   -------------    -------------    ---------------
                                                                                
Actual (1.62% return)                                $ 1,000.00       $ 1,016.20         $ 3.85
Hypothetical (5% annual return before expenses)      $ 1,000.00       $ 1,021.66         $ 3.86
</Table>

- ----------
  *  EXPENSES ARE EQUAL TO THE FUND'S ANNUALIZED EXPENSE RATIO OF 0.75%
     MULTIPLIED BY THE AVERAGE ACCOUNT VALUE OVER THE PERIOD, MULTIPLIED BY
     186/365 (TO REFLECT THE ONE-HALF YEAR PERIOD). IF THE FUND HAD BORNE ALL OF
     ITS EXPENSES THAT WERE REIMBURSED OR WAIVED BY THE INVESTMENT ADVISER AND
     ADMINISTRATOR, THE ANNUALIZED EXPENSE RATIO WOULD HAVE BEEN 0.77%.

                                        4
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
PORTFOLIO OF INVESTMENTS - JANUARY 31, 2006

<Table>
<Caption>
                                                                 ANNUALIZED
PRINCIPAL                                                          YIELD
AMOUNT IN                                                        ON DATE OF        MATURITY
THOUSANDS  DESCRIPTION                                            PURCHASE           DATE               VALUE
- -----------------------------------------------------------------------------------------------------------------
                                                                                       
           U.S. GOVERNMENT AGENCY - DISCOUNT NOTES (64.9%)
$  25,000  Federal Farm Credit Banks                                4.19%          02/08/06        $   24,979,729
  397,573  Federal Home Loan Banks                               4.23 - 4.52  02/03/06 - 06/07/06     395,631,939
   91,913  Federal Home Loan Mortgage Corp.                      4.37 - 4.61  03/27/06 - 07/18/06      90,716,177
   97,574  Federal National Mortgage Assoc.                      4.12 - 4.65  02/01/06 - 07/26/06      96,925,008
                                                                                                   --------------
           TOTAL U.S. GOVERNMENT AGENCY - DISCOUNT NOTES
             (COST $608,252,853)                                                                      608,252,853
                                                                                                   --------------
           U.S. GOVERNMENT AGENCY - FLOATING RATE NOTES (17.4%)
   48,900  Federal Farm Credit Banks                             4.29 - 4.42  02/21/06 - 08/01/06      48,897,983
  114,000  Federal Home Loan Banks                               4.14 - 4.39  05/10/06 - 08/21/06     113,991,261
                                                                                                   --------------
           TOTAL U.S. GOVERNMENT AGENCY - FLOATING RATE NOTES
             (COST $162,889,244)                                                                      162,889,244
                                                                                                   --------------
           REPURCHASE AGREEMENTS (18.2%)
   35,000  Banc of America Securities, LLC (dated
             01/31/06; proceeds $35,004,307) (a)                    4.43            02/01/06           35,000,000
   75,000  Deutsche Bank Securities, Inc. (dated
             01/31/06; proceeds $75,009,292) (b)                    4.46            02/01/06           75,000,000
   30,000  Goldman Sachs Group, Inc. (The) (dated
             1/26/06; proceeds $30,025,783) (c)                     4.42            02/02/06           30,000,000
   30,000  Goldman Sachs Group, Inc. (The) (dated
             1/23/06; proceeds $30,050,750) (d)                     4.35            02/06/06           30,000,000
    1,078  The Bank of New York (dated
             01/31/06; proceeds $1,077,941) (e)                     4.313           02/01/06            1,077,812
                                                                                                   --------------
           TOTAL REPURCHASE AGREEMENTS
             (COST $171,077,812)                                                                      171,077,812
                                                                                                   --------------
           U.S. GOVERNMENT OBLIGATION (0.6%)
    6,000  U.S. Treasury Bill (COST $5,994,773)                     3.93            02/09/06            5,994,773
                                                                                                   --------------
           TOTAL INVESTMENTS (COST $948,214,682) (f)                                  101.1%          948,214,682
           LIABILITIES IN EXCESS OF OTHER ASSETS                                       (1.1)          (10,389,424)
                                                                                      -----        --------------
           NET ASSETS                                                                 100.0%       $  937,825,258
                                                                                      =====        ==============
</Table>

- ----------
   (a)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 5.00 - 5.50% DUE
        01/01/19 - 03/01/20 VALUED AT $35,700,001.
   (b)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 6.50% DUE 05/01/23
        VALUED AT $27,732,967 AND FEDERAL MORTGAGE ACCEPTANCE CORP. 4.00 - 5.50%
        DUE 08/01/20 - 05/01/25 VALUED AT $48,767,033.
   (c)  COLLATERALIZED BY U.S. TREASURY TINTS 0.00% DUE 05/15/21 VALUED AT
        $30,600,000.
   (d)  COLLATERALIZED BY U.S. TREASURY TINTS 0.00% DUE 11/15/17 - 05/15/21
        VALUED AT $30,600,000.
   (e)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 5.50% DUE 08/01/35
        VALUED AT $1,099,368.
   (f)  COST IS THE SAME FOR FEDERAL INCOME TAX PURPOSES.

                        SEE NOTES TO FINANCIAL STATEMENTS

                                        5
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL STATEMENTS

STATEMENT OF ASSETS AND LIABILITIES
JANUARY 31, 2006

<Table>
                                                                              
ASSETS:
Investments in securities, at value (cost $948,214,682)
  (including repurchase agreements of $171,077,812)                              $  948,214,682
Cash                                                                                     90,000
Receivable for:
    Interest                                                                            901,566
    Shares of beneficial interest sold                                                    6,852
Prepaid expenses and other assets                                                        40,273
                                                                                 --------------
    TOTAL ASSETS                                                                    949,253,373
                                                                                 --------------
LIABILITIES:
Payable for:
    Shares of beneficial interest redeemed                                           10,791,906
    Investment advisory fee                                                             317,316
    Distribution fee                                                                     63,109
    Transfer agent fee                                                                   48,315
    Administration fee                                                                   41,748
Accrued expenses and other payables                                                     165,721
                                                                                 --------------
    TOTAL LIABILITIES                                                                11,428,115
                                                                                 --------------
    NET ASSETS                                                                   $  937,825,258
                                                                                 ==============
COMPOSITION OF NET ASSETS:
Paid-in-capital                                                                  $  937,738,851
Accumulated undistributed net investment income                                          86,407
                                                                                 --------------
    NET ASSETS                                                                   $  937,825,258
                                                                                 ==============
NET ASSET VALUE PER SHARE
937,803,763 shares outstanding (UNLIMITED SHARES AUTHORIZED OF $.01 PAR VALUE)   $         1.00
                                                                                 ==============
</Table>

                        SEE NOTES TO FINANCIAL STATEMENTS

                                        6
<Page>

STATEMENT OF OPERATIONS
FOR THE YEAR ENDED JANUARY 31, 2006

<Table>
                                                                              
NET INVESTMENT INCOME:

INTEREST INCOME                                                                  $   34,228,165
                                                                                 --------------
EXPENSES
Investment advisory fee                                                               4,045,523
Transfer agent fees and expenses                                                      1,799,172
Distribution fee                                                                        995,958
Administration fee                                                                      508,173
Shareholder reports and notices                                                         164,497
Professional fees                                                                        65,142
Registration fees                                                                        60,443
Custodian fees                                                                           52,107
Trustees' fees and expenses                                                              21,236
Other                                                                                    56,315
                                                                                 --------------
    TOTAL EXPENSES                                                                    7,768,566
Less: amounts waived/reimbursed                                                        (168,052)
                                                                                 --------------
    NET EXPENSES                                                                      7,600,514
                                                                                 --------------
NET INVESTMENT INCOME                                                            $   26,627,651
                                                                                 ==============
</Table>

                        SEE NOTES TO FINANCIAL STATEMENTS

                                        7
<Page>

STATEMENT OF CHANGES IN NET ASSETS

<Table>
<Caption>
                                                                    FOR THE YEAR        FOR THE YEAR
                                                                       ENDED               ENDED
                                                                  JANUARY 31, 2006    JANUARY 31, 2005
                                                                  ----------------    ----------------
                                                                                
INCREASE (DECREASE) IN NET ASSETS:
OPERATIONS:
Net investment income                                             $     26,627,651    $      8,941,329
Dividends to shareholders from net investment income                   (26,626,357)         (8,966,340)
Net decrease from transactions in shares of beneficial interest       (184,921,785)       (146,513,383)
                                                                  ----------------    ----------------

    NET DECREASE                                                      (184,920,491)       (146,538,394)

NET ASSETS:
Beginning of period                                                  1,122,745,749       1,269,284,143
                                                                  ----------------    ----------------
END OF PERIOD
(INCLUDING ACCUMULATED UNDISTRIBUTED NET INVESTMENT INCOME OF
  $86,407 AND $85,113, RESPECTIVELY)                              $    937,825,258    $  1,122,745,749
                                                                  ================    ================
</Table>

                        SEE NOTES TO FINANCIAL STATEMENTS

                                        8
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
NOTES TO FINANCIAL STATEMENTS - JANUARY 31, 2006

1. ORGANIZATION AND ACCOUNTING POLICIES
Morgan Stanley U.S. Government Money Market Trust (the "Fund") is registered
under the Investment Company Act of 1940, as amended (the "Act"), as a
diversified, open-end management investment company. The Fund's investment
objectives are security of principal, high current income and liquidity. The
Fund was organized as a Massachusetts business trust on November 18, 1981 and
commenced operations on February 17, 1982.

The following is a summary of significant accounting policies:

A. VALUATION OF INVESTMENTS -- Portfolio securities are valued at amortized
cost, which approximates market value, in accordance with Rule 2a-7 of the
Investment Company Act of 1940.

B. ACCOUNTING FOR INVESTMENTS -- Security transactions are accounted for on the
trade date (date the order to buy or sell is executed). Realized gains and
losses on security transactions are determined by the identified cost method.
Discounts are accreted and premiums are amortized over the life of the
respective securities. Interest income is accrued daily.

C. REPURCHASE AGREEMENTS -- The Fund may invest directly with institutions in
repurchase agreements. The Fund's custodian receives the collateral, which is
marked-to-market daily to determine that the value of the collateral does not
decrease below the repurchase price plus accrued interest.

D. FEDERAL INCOME TAX POLICY -- It is the Fund's policy to comply with the
requirements of the Internal Revenue Code applicable to regulated investment
companies and to distribute substantially all of its taxable income to its
shareholders. Accordingly, no federal income tax provision is required.

E. DIVIDENDS AND DISTRIBUTIONS TO SHAREHOLDERS -- The Fund records dividends and
distributions to shareholders as of the close of each business day.

F. USE OF ESTIMATES -- The preparation of financial statements in accordance
with generally accepted accounting principles requires management to make
estimates and assumptions that affect the reported amounts and disclosures.
Actual results could differ from those estimates.

2. INVESTMENT ADVISORY/ADMINISTRATION AGREEMENTS
Pursuant to an Investment Advisory Agreement with Morgan Stanley Investment
Advisors Inc. (the "Investment Adviser"), the Fund pays the Investment Adviser
an advisory fee, accrued daily and payable monthly, by applying the following
annual rates to the net assets of the Fund determined as of the close of each
business day: 0.45% to the portion of the daily net assets not exceeding $500
million; 0.375% to the portion of the daily net assets exceeding $500 million
but not exceeding $750 million; 0.325% to the portion of the daily net assets
exceeding $750 million but not exceeding $1 billion; 0.30% to the portion of the
daily net assets exceeding $1 billion but not exceeding $1.5 billion; 0.275% to
the

                                        9
<Page>

portion of the daily net assets exceeding $1.5 billion but not exceeding $2
billion; 0.25% to the portion of the daily net assets exceeding $2 billion but
not exceeding $2.5 billion; 0.225% to the portion of the daily net assets
exceeding $2.5 billion but not exceeding $3 billion; and 0.20% to the portion of
the daily net assets exceeding $3 billion.

Pursuant to an Administration Agreement with Morgan Stanley Services Company
Inc. (the "Administrator"), an affiliate of the Investment Adviser, the Fund
pays an administration fee, accrued daily and payable monthly, by applying the
annual rate of 0.05% to the Fund's daily net assets.

For the year ended January 31, 2006 and through April 30, 2006, the Investment
Adviser agreed to waive its fee and reimburse expenses to the extent they exceed
0.75% of the daily net assets of the Fund.

3. PLAN OF DISTRIBUTION
Morgan Stanley Distributors Inc. (the "Distributor"), an affiliate of the
Investment Adviser and Administrator, is the distributor of the Fund's shares
and in accordance with a Plan of Distribution (the "Plan") pursuant to Rule
12b-1 under the Act, finances certain expenses in connection with the promotion
of sales of Fund shares.

Reimbursements for these expenses are made in monthly payments by the Fund to
the Distributor, which will in no event exceed an amount equal to a payment at
the annual rate of 0.15% of the Fund's average daily net assets during the
month. Expenses incurred by the Distributor pursuant to the Plan in any fiscal
year will not be reimbursed by the Fund through payments accrued in any
subsequent fiscal year. For the year ended January 31, 2006, the distribution
fee was accrued at the annual rate of 0.10%.

4. SECURITY TRANSACTIONS AND TRANSACTIONS WITH AFFILIATES
The cost of purchases and proceeds from sales/maturities of portfolio securities
for the year ended January 31, 2006 aggregated $32,457,850,572 and
$32,664,221,565, respectively.

Morgan Stanley Trust, an affiliate of the Investment Adviser, Administrator and
Distributor, is the Fund's transfer agent.

The Fund has an unfunded noncontributory defined benefit pension plan covering
certain independent Trustees of the Fund who will have served as independent
Trustees for at least five years at the time of retirement. Benefits under this
plan are based on factors which include years of service and compensation. The
Trustees voted to close the plan to new participants and eliminate the future
benefits growth due to increases to compensation after July 31, 2003. Aggregate
pension costs for the year ended January 31, 2006 included in Trustees' fees and
expenses in the Statement of Operations amounted to $7,373. At January 31, 2006,
the Fund had an accrued pension liability of $62,456 which is included in
accrued expenses in the Statement of Assets and Liabilities.

                                       10
<Page>

The Fund has an unfunded Deferred Compensation Plan (the "Compensation Plan")
which allows each independent Trustee to defer payment of all, or a portion, of
the fees he receives for serving on the Board of Trustees. Each eligible Trustee
generally may elect to have the deferred amounts credited with a return equal to
the total return on one or more of the Morgan Stanley funds that are offered as
investment options under the Compensation Plan. Appreciation/depreciation and
distributions received from these investments are recorded with an offsetting
increase/decrease in the deferred compensation obligation and do not affect the
net asset value of the Fund.

5. SHARES OF BENEFICIAL INTEREST
Transactions in shares of beneficial interest, at $1.00 per share, were as
follows:

<Table>
<Caption>
                                                                    FOR THE YEAR        FOR THE YEAR
                                                                       ENDED               ENDED
                                                                  JANUARY 31, 2006    JANUARY 31, 2005
                                                                  ----------------    ----------------
                                                                                  
Shares sold                                                          2,112,793,188       2,729,300,423
Shares issued in reinvestment of dividends                              26,500,899           8,935,675
                                                                  ----------------    ----------------
                                                                     2,139,294,087       2,738,236,098
Shares redeemed                                                     (2,324,215,872)     (2,884,749,481)
                                                                  ----------------    ----------------
Net decrease                                                          (184,921,785)       (146,513,383)
                                                                  ================    ================
</Table>

6. LEGAL MATTERS
The Investment Adviser, certain affiliates of the Investment Adviser, certain
officers of such affiliates and certain investment companies advised by the
Investment Adviser or its affiliates, including the Fund, are named as
defendants in a consolidated class action. This consolidated action also names
as defendants certain individual Trustees and Directors of the Morgan Stanley
funds. The consolidated amended complaint, filed in the United States District
Court Southern District of New York on April 16, 2004, generally alleges that
defendants, including the Fund, violated their statutory disclosure obligations
and fiduciary duties by failing properly to disclose (i) that the Investment
Adviser and certain affiliates of the Investment Adviser allegedly offered
economic incentives to brokers and others to recommend the funds advised by the
Investment Adviser or its affiliates to investors rather than funds managed by
other companies, and (ii) that the funds advised by the Investment Adviser or
its affiliates, including the Fund, allegedly paid excessive commissions to
brokers in return for their efforts to recommend these funds to investors. The
complaint seeks, among other things, unspecified compensatory damages,
rescissionary damages, fees and costs. The defendants have moved to dismiss the
action and intend to otherwise vigorously defend it. On March 9, 2005,
Plaintiffs sought leave to supplement their complaint to assert claims on behalf
of other investors. While the Fund and Adviser believe that each has meritorious
defenses, the ultimate outcome of this matter is not presently determinable at
this stage of the litigation, and no provision has been made in the Fund's
financial statements for the effect, if any, of this matter.

                                       11
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
FINANCIAL HIGHLIGHTS

Selected ratios and per share data for a share of beneficial interest
outstanding throughout each period:

<Table>
<Caption>
                                                                        FOR THE YEAR ENDED JANUARY 31,
                                                   --------------------------------------------------------------------------
                                                      2006             2005          2004             2003            2002
                                                   ---------        ---------     ---------        ---------        ---------
                                                                                                     
SELECTED PER SHARE DATA:
Net asset value, beginning of period               $    1.00        $    1.00     $    1.00        $    1.00        $    1.00
                                                   ---------        ---------     ---------        ---------        ---------
Net investment income from investment operations       0.027            0.008         0.004            0.011            0.032
Less dividends from net investment income             (0.027)          (0.008)       (0.004)          (0.011)          (0.032)
                                                   ---------        ---------     ---------        ---------        ---------

Net asset value, end of period                     $    1.00        $    1.00     $    1.00        $    1.00        $    1.00
                                                   =========        =========     =========        =========        =========

TOTAL RETURN                                            2.71%            0.78%         0.45%            1.06%            3.25%

RATIOS TO AVERAGE NET ASSETS:
Expenses                                                0.75%(1)         0.73%         0.71%(1)         0.74%(1)         0.74%(1)
Net investment income                                   2.62%(1)         0.74%         0.43%(1)         1.03%(1)         3.14%(1)

SUPPLEMENTAL DATA:
Net assets, end of period, in millions             $     938        $   1,123     $   1,269        $   1,340        $   1,257
</Table>

- ----------
(1)  IF THE FUND HAD BORNE ALL ITS EXPENSES THAT WERE REIMBURSED OR WAIVED BY
     THE INVESTMENT ADVISER AND ADMINISTRATOR, THE ANNUALIZED EXPENSE AND NET
     INVESTMENT INCOME RATIOS WOULD HAVE BEEN AS FOLLOWS:

<Table>
<Caption>
                                               EXPENSE   NET INVESTMENT
                              PERIOD ENDED      RATIO     INCOME RATIO
                            ----------------   -------   --------------
                                                         
                            JANUARY 31, 2006     0.76%         2.60%
                            JANUARY 31, 2004     0.71          0.43
                            JANUARY 31, 2003     0.76          1.01
                            JANUARY 31, 2002     0.81          3.07
</Table>

                        SEE NOTES TO FINANCIAL STATEMENTS

                                       12
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
REPORT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

TO THE SHAREHOLDERS AND BOARD OF TRUSTEES OF
MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST:

We have audited the accompanying statement of assets and liabilities of Morgan
Stanley U.S. Government Money Market Trust (the "Fund"), including the portfolio
of investments, as of January 31, 2006, and the related statements of operations
for the year then ended and changes in net assets for each of the two years in
the period then ended, and the financial highlights for each of the five years
in the period then ended. These financial statements and financial highlights
are the responsibility of the Fund's management. Our responsibility is to
express an opinion on these financial statements and financial highlights based
on our audits.

We conducted our audits in accordance with the standards of the Public Company
Accounting Oversight Board (United States). Those standards require that we plan
and perform the audit to obtain reasonable assurance about whether the financial
statements and financial highlights are free of material misstatement. The Fund
is not required to have, nor were we engaged to perform, an audit of its
internal control over financial reporting. Our audits included consideration of
internal control over financial reporting as a basis for designing audit
procedures that are appropriate in the circumstances, but not for the purpose of
expressing an opinion on the effectiveness of the Fund's internal control over
financial reporting. Accordingly, we express no such opinion. An audit also
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the financial statements, assessing the accounting principles
used and significant estimates made by management, as well as evaluating the
overall financial statement presentation. Our procedures included confirmation
of securities owned as of January 31, 2006, by correspondence with the custodian
and brokers; where replies were not received from brokers, we performed other
auditing procedures. We believe that our audits provide a reasonable basis for
our opinion.

In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of Morgan
Stanley U.S. Government Money Market Trust as of January 31, 2006, the results
of its operations for the year then ended, the changes in its net assets for
each of the two years in the period then ended, and the financial highlights for
each of the five years in the period then ended, in conformity with accounting
principles generally accepted in the United States of America.


DELOITTE & TOUCHE LLP
NEW YORK, NEW YORK
MARCH 23, 2006

                                       13
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST
TRUSTEE AND OFFICER INFORMATION

INDEPENDENT TRUSTEES:

<Table>
<Caption>
                                                                                                  NUMBER OF
                                                                                                 PORTFOLIOS
                                                       TERM OF                                     IN FUND
                                        POSITION(S)  OFFICE AND                                    COMPLEX
       NAME, AGE AND ADDRESS OF          HELD WITH    LENGTH OF  PRINCIPAL OCCUPATION(S) DURING   OVERSEEN     OTHER DIRECTORSHIPS
         INDEPENDENT TRUSTEE            REGISTRANT  TIME SERVED*          PAST 5 YEARS**        BY TRUSTEE***    HELD BY TRUSTEE
- --------------------------------------- ----------- ------------ ------------------------------ ------------- --------------------
                                                                                               
Michael Bozic (65)                      Trustee     Since        Private Investor; Director or  197           Director of various
c/o Kramer Levin Naftalis & Frankel LLP             April 1994   Trustee of the Retail Funds                  business
Counsel to the Independent Trustees                              (since April 1994) and the                   organizations.
1177 Avenue of the Americas                                      Institutional Funds (since
New York, NY 10036                                               July 2003); formerly Vice
                                                                 Chairman of Kmart Corporation
                                                                 (December 1998-October 2000),
                                                                 Chairman and Chief Executive
                                                                 Officer of Levitz Furniture
                                                                 Corporation (November
                                                                 1995-November 1998) and
                                                                 President and Chief Executive
                                                                 Officer of Hills Department
                                                                 Stores (May 1991-July 1995);
                                                                 formerly variously Chairman,
                                                                 Chief Executive Officer,
                                                                 President and Chief Operating
                                                                 Officer (1987-1991) of the
                                                                 Sears Merchandise Group of
                                                                 Sears, Roebuck & Co.

Edwin J. Garn (73)                      Trustee     Since        Consultant; Director or        197           Director of Franklin
1031 N. Chartwell Court                             January 1993 Trustee of the Retail Funds                  Covey (time
Salt Lake City, UT 84103                                         (since January 1993) and the                 management systems),
                                                                 Institutional Funds (since                   BMW Bank of North
                                                                 July 2003); member of the Utah               America, Inc.
                                                                 Regional Advisory Board of                   (industrial loan
                                                                 Pacific Corp. (utility                       corporation), Escrow
                                                                 company); formerly Managing                  Bank USA (industrial
                                                                 Director of Summit Ventures                  loan corporation),
                                                                 LLC (2000-2004) (lobbying and                United Space
                                                                 consulting firm); United                     Alliance (joint
                                                                 States Senator (R-Utah)                      venture between
                                                                 (1974-1992) and Chairman,                    Lockheed Martin and
                                                                 Senate Banking Committee                     the Boeing Company)
                                                                 (1980-1986), Mayor of Salt                   and Nuskin Asia
                                                                 Lake City, Utah (1971-1974),                 Pacific (multilevel
                                                                 Astronaut, Space Shuttle                     marketing); member
                                                                 Discovery (April 12-19, 1985),               of the board of
                                                                 and Vice Chairman, Huntsman                  various civic and
                                                                 Corporation (chemical                        charitable
                                                                 company).                                    organizations.

Wayne E. Hedien (71)                    Trustee     Since        Retired; Director or Trustee   197           Director of The PMI
c/o Kramer Levin Naftalis & Frankel LLP             September    of the Retail Funds (since                   Group Inc. (private
Counsel to the Independent Trustees                 1997         September 1997) and the                      mortgage insurance);
1177 Avenue of the Americas                                      Institutional Funds (since                   Trustee and Vice
New York, NY 10036                                               July 2003); formerly                         Chairman of The
                                                                 associated with the Allstate                 Field Museum of
                                                                 Companies (1966-1994), most                  Natural History;
                                                                 recently as Chairman of The                  director of various
                                                                 Allstate Corporation (March                  other business and
                                                                 1993-December 1994) and                      charitable
                                                                 Chairman and Chief Executive                 organizations.
                                                                 Officer of its wholly-owned
                                                                 subsidiary, Allstate Insurance
                                                                 Company (July 1989-December
                                                                 1994).
</Table>

                                       14
<Page>

<Table>
<Caption>
                                                                                                  NUMBER OF
                                                                                                 PORTFOLIOS
                                                       TERM OF                                     IN FUND
                                        POSITION(S)  OFFICE AND                                    COMPLEX
       NAME, AGE AND ADDRESS OF          HELD WITH    LENGTH OF  PRINCIPAL OCCUPATION(S) DURING   OVERSEEN     OTHER DIRECTORSHIPS
         INDEPENDENT TRUSTEE            REGISTRANT  TIME SERVED*          PAST 5 YEARS**        BY TRUSTEE***    HELD BY TRUSTEE
- --------------------------------------- ----------- ------------ ------------------------------ ------------- --------------------
                                                                                               
Dr. Manuel H. Johnson (56)              Trustee     Since        Senior Partner, Johnson        197           Director of NVR,
c/o Johnson Smick Group, Inc.                       July 1991    Smick International, Inc., a                 Inc. (home
888 16th Street, NW                                              consulting firm; Chairman of                 construction);
Suite 740                                                        the Audit Committee and                      Director of KFX
Washington, D.C. 20006                                           Director or Trustee of the                   Energy; Director of
                                                                 Retail Funds (since July                     RBS Greenwich
                                                                 1991) and the Institutional                  Capital Holdings
                                                                 Funds (since July 2003);                     (financial holding
                                                                 Co-Chairman and a founder of                 company).
                                                                 the Group of Seven Council
                                                                 (G7C), an international
                                                                 economic commission;
                                                                 formerly Vice Chairman of
                                                                 the Board of Governors of
                                                                 the Federal Reserve System
                                                                 and Assistant Secretary of
                                                                 the U.S. Treasury.

Joseph J. Kearns (63)                   Trustee     Since        President, Kearns &            198           Director of Electro
c/o Kearns & Associates LLC                         July 2003    Associates LLC (investment                   Rent Corporation
PMB754                                                           consulting); Deputy Chairman                 (equipment leasing),
23852 Pacific Coast Highway                                      of the Audit Committee and                   The Ford Family
Malibu, CA 90265                                                 Director or Trustee of the                   Foundation, and the
                                                                 Retail Funds (since July                     UCLA Foundation.
                                                                 2003) and the Institutional
                                                                 Funds (since August 1994);
                                                                 previously Chairman of the
                                                                 Audit Committee of the
                                                                 Institutional Funds (October
                                                                 2001-July 2003); formerly
                                                                 CFO of the J. Paul Getty
                                                                 Trust.

Michael E. Nugent (69)                  Trustee     Since        General Partner of Triumph     197           None.
c/o Triumph Capital, L.P.                           July 1991    Capital, L.P., a private
445 Park Avenue                                                  investment partnership;
New York, NY 10022                                               Chairman of the Insurance
                                                                 Committee and Director or
                                                                 Trustee of the Retail Funds
                                                                 (since July 1991) and the
                                                                 Institutional Funds (since
                                                                 July 2001); formerly Vice
                                                                 President, Bankers Trust
                                                                 Company and BT Capital
                                                                 Corporation (1984-1988).

Fergus Reid (73)                        Trustee     Since        Chairman of Lumelite           198           Trustee and Director
c/o Lumelite Plastics Corporation                   July 2003    Plastics Corporation;                        of certain
85 Charles Colman Blvd.                                          Chairman of the Governance                   investment companies
Pawling, NY 12564                                                Committee and Director or                    in the JPMorgan
                                                                 Trustee of the Retail Funds                  Funds complex
                                                                 (since July 2003) and the                    managed by J.P.
                                                                 Institutional Funds (since                   Morgan Investment
                                                                 June 1992).                                  Management Inc.
</Table>

                                       15
<Page>

INTERESTED TRUSTEES:

<Table>
<Caption>
                                                                                                  NUMBER OF
                                                                                                 PORTFOLIOS
                                                       TERM OF                                     IN FUND
                                        POSITION(S)  OFFICE AND                                    COMPLEX
       NAME, AGE AND ADDRESS OF          HELD WITH    LENGTH OF  PRINCIPAL OCCUPATION(S) DURING   OVERSEEN     OTHER DIRECTORSHIPS
          INTERESTED TRUSTEE            REGISTRANT  TIME SERVED*          PAST 5 YEARS**        BY TRUSTEE***    HELD BY TRUSTEE
- --------------------------------------- ----------- ------------ ------------------------------ ------------- --------------------
                                                                                               
Charles A. Fiumefreddo (72)             Chairman of Since        Chairman and Director or       197           None.
c/o Morgan Stanley Trust                the Board   July 1991    Trustee of the Retail Funds
Harborside Financial Center,            and Trustee              (since July 1991) and the
Plaza Two,                                                       Institutional Funds (since
Jersey City, NJ 07311                                            July 2003); formerly Chief
                                                                 Executive Officer of the
                                                                 Retail Funds (until
                                                                 September 2002).

James F. Higgins (57)                   Trustee     Since        Director or Trustee of the     197           Director of AXA
c/o Morgan Stanley Trust                            June 2000    Retail Funds (since June                     Financial, Inc. and
Harborside Financial Center,                                     2000) and the Institutional                  The Equitable Life
Plaza Two,                                                       Funds (since July 2003);                     Assurance Society of
Jersey City, NJ 07311                                            Senior Advisor of Morgan                     the United States
                                                                 Stanley (since August 2000);                 (financial
                                                                 Director of Dean Witter                      services).
                                                                 Realty Inc.
</Table>

- ----------
   * THIS IS THE EARLIEST DATE THE TRUSTEE BEGAN SERVING THE FUNDS ADVISED BY
     MORGAN STANLEY INVESTMENT ADVISORS INC. (THE "INVESTMENT ADVISER") (THE
     "RETAIL FUNDS").
  ** THE DATES REFERENCED BELOW INDICATING COMMENCEMENT OF SERVICES AS
     DIRECTOR/TRUSTEE FOR THE RETAIL FUNDS AND THE FUNDS ADVISED BY MORGAN
     STANLEY INVESTMENT MANAGEMENT INC. AND MORGAN STANLEY AIP GP LP (THE
     "INSTITUTIONAL FUNDS") REFLECT THE EARLIEST DATE THE DIRECTOR/TRUSTEE BEGAN
     SERVING THE RETAIL OR INSTITUTIONAL FUNDS, AS APPLICABLE.
 *** THE FUND COMPLEX INCLUDES ALL OPEN-END AND CLOSED-END FUNDS (INCLUDING ALL
     OF THEIR PORTFOLIOS) ADVISED BY THE INVESTMENT ADVISER AND ANY FUNDS THAT
     HAVE AN INVESTMENT ADVISER THAT IS AN AFFILIATED PERSON OF THE INVESTMENT
     ADVISER (INCLUDING, BUT NOT LIMITED TO, MORGAN STANLEY INVESTMENT
     MANAGEMENT INC.).

                                       16
<Page>

OFFICERS:

<Table>
<Caption>
                                                    TERM OF
                                  POSITION(S)      OFFICE AND
  NAME, AGE AND ADDRESS OF         HELD WITH       LENGTH OF
     EXECUTIVE OFFICER            REGISTRANT      TIME SERVED*              PRINCIPAL OCCUPATION(S) DURING PAST 5 YEARS**
- ------------------------------  --------------  ----------------  -----------------------------------------------------------------
                                                         
Ronald E. Robison (67)          President and   Since May 2003    President (since September 2005) and Principal Executive Officer
1221 Avenue of the Americas     Principal                         (since May 2003) of funds in the Fund Complex; President (since
New York, NY 10020              Executive                         September 2005) and Principal Executive Officer (since May 2003)
                                Officer                           of the Van Kampen Funds; Managing Director of Morgan Stanley,
                                                                  Morgan Stanley Investment Management and Morgan Stanley & Co.
                                                                  Incorporated; Managing Director and Director of Morgan Stanley
                                                                  Investment Advisors Inc.; Managing Director and (since May 2002)
                                                                  Director , Morgan Stanley Investment Management Inc., Managing
                                                                  Director and (since January 2005) Director of Van Kampen Asset
                                                                  Management and Van Kampen Investments Inc. Director, President
                                                                  (since February 2006) and Chief Executive Officer (since February
                                                                  2006) of Morgan Stanley Services Company Inc., Director of Morgan
                                                                  Stanley Distributors Inc., Morgan Stanley Distribution, Inc. and
                                                                  Morgan Stanley Trust; Director of Morgan Stanley SICAV (since May
                                                                  2004). Formerly, Executive Vice President (July 2003 to September
                                                                  2005) of funds in the Fund Complex and the Van Kampen Funds;
                                                                  President and Director of the Institutional Funds (March
                                                                  2001-July 2003), Chief Global Operating Officer of Morgan Stanley
                                                                  Investment Management Inc., Chief Administrative Officer of
                                                                  Morgan Stanley Investment Advisors Inc.; Chief Administrative
                                                                  Officer of Morgan Stanley Services Company Inc. (November 2003 to
                                                                  February 2006).

J. David Germany (51)           Vice President  Since             Managing Director and (since December 2005) Chief Investment
25 Cabot Square, Canary Wharf,                  February 2006     Officer - Global Fixed Income of Morgan Stanley Investment
London, United Kingdom                                            Advisors Inc., Morgan Stanley Investment Management Inc., Van
E144QA                                                            Kampen Asset Management and Van Kampen Advisors Inc. Managing
                                                                  Director and Director of Morgan Stanley Investment Management
                                                                  Ltd. Vice President (since February 2006) of the Retail and
                                                                  Institutional Funds.

Dennis F. Shea (52)             Vice President  Since             Managing Director and (since February 2006) Chief Investment
1221 Avenue of the Americas                     February 2006     Officer - Global Equity of Morgan Stanley Investment Advisors
New York, NY 10020                                                Inc., Morgan Stanley Investment Management Inc., Van Kampen Asset
                                                                  Management and Van Kampen Advisors Inc. Vice President (since
                                                                  February 2006) of the Retail and Institutional Funds. Formerly,
                                                                  Managing Director and Director of Global Equity Research at
                                                                  Morgan Stanley.

Barry Fink (51)                 Vice President  Since             Managing Director of Morgan Stanley Investment Management, Morgan
1221 Avenue of the Americas                     February 1997     Stanley Investment Advisors Inc. and Morgan Stanley Investment
New York, NY 10020                                                Management Inc.; Vice President of the Retail Funds and (since
                                                                  July 2003) the Institutional Funds; Formerly, General Counsel
                                                                  (May 2000-February 2006) of Morgan Stanley Investment Management;
                                                                  Secretary (October 2003 to February 2006), General Counsel (May
                                                                  2004 to February 2006) and Director (July 1998 to January 2005)
                                                                  of Morgan Stanley Investment Advisors Inc. and Morgan Stanley
                                                                  Services Company Inc.; Secretary and General Counsel of Morgan
                                                                  Stanley Investment Management Inc. (November 2002 to February
                                                                  2006); Secretary and Director of Morgan Stanley Distributors
                                                                  Inc.; Secretary (February 1997 to July 2003) and General Counsel
                                                                  (February 1997 to April 2004) of the Morgan Stanley Retail Funds;
                                                                  Vice President and Assistant General Counsel of Morgan Stanley
                                                                  Investment Advisors Inc. and Morgan Stanley Distributors Inc.
                                                                  (February 1997 to December 2001).
</Table>

                                       17
<Page>

<Table>
<Caption>
                                                    TERM OF
                                  POSITION(S)      OFFICE AND
  NAME, AGE AND ADDRESS OF         HELD WITH       LENGTH OF
     EXECUTIVE OFFICER            REGISTRANT      TIME SERVED*              PRINCIPAL OCCUPATION(S) DURING PAST 5 YEARS**
- ------------------------------  --------------  ----------------  -----------------------------------------------------------------
                                                         
Amy R. Doberman (43)            Vice President  Since July 2004   Managing Director and General Counsel, U.S. Investment Management
1221 Avenue of the Americas                                       (since July 2004); Vice President of the Retail Funds and the
New York, NY 10020                                                Institutional Funds (since July 2004); Vice President of the Van
                                                                  Kampen Funds (since August 2004); Secretary (since February 2006)
                                                                  and Managing Director (since July 2004) of Morgan Stanley
                                                                  Investment Advisors Inc., Morgan Stanley Services Company Inc.,
                                                                  Morgan Stanley Investment Management Inc., Van Kampen Asset
                                                                  Management, Van Kampen Advisors Inc. and Van Kampen Investments
                                                                  Inc.; Secretary (since February 2006) of Morgan Stanley
                                                                  Distributors Inc. and Morgan Stanley Distribution, Inc. Formerly,
                                                                  Managing Director and General Counsel - Americas, UBS Global
                                                                  Asset Management (July 2000 to July 2004).

Carsten Otto (42)               Chief           Since             Managing Director and U.S. Director of Compliance for Morgan
1221 Avenue of the Americas     Compliance      October 2004      Stanley Investment Management (since October 2004); Managing
New York, NY 10020              Officer                           Director and Chief Compliance Officer (since February 2005) of
                                                                  Morgan Stanley Investment Advisors Inc. and Morgan Stanley
                                                                  Investment Management Inc. and (since June 2004) of Van Kampen
                                                                  Asset Management, Van Kampen Advisors Inc. and Van Kampen
                                                                  Investments Inc. Formerly, Assistant Secretary and Assistant
                                                                  General Counsel of the Retail Funds.

Stefanie V. Chang (39)          Vice President  Since July 2003   Executive Director of Morgan Stanley & Co. Incorporated, Morgan
1221 Avenue of the Americas                                       Stanley Investment Advisors Inc., Morgan Stanley Investment
New York, NY 10020                                                Management Inc., Van Kampen Asset Management, Van Kampen Advisors
                                                                  Inc. and Van Kampen Investments Inc. Vice President of the Retail
                                                                  Funds (since July 2002) and the Institutional Funds (since
                                                                  December 1997). Formerly, Secretary of Van Kampen Asset
                                                                  Management Inc., Van Kampen Advisors Inc. and Van Kampen
                                                                  Investments Inc. (December 2002 to February 2006); Secretary of
                                                                  Morgan Stanley Distribution, Inc. (October 2005 to February
                                                                  2006).

Francis J. Smith (40)           Treasurer and   Treasurer since   Executive Director of Morgan Stanley Investment Advisors Inc. and
c/o Morgan Stanley Trust        Chief           July 2003 and     Morgan Stanley Services Company Inc.; Treasurer and Chief
Harborside Financial Center,    Financial       Chief Financial   Financial Officer of the Morgan Stanley Retail Funds (since July
Plaza Two,                      Officer         Officer since     2003). Formerly Vice President of the Retail Funds (September
Jersey City, NJ 07311                           September 2002    2002-July 2003).

Thomas F. Caloia (59)           Vice President  Since July 2003   Executive Director of Morgan Stanley Investment Advisors Inc. and
c/o Morgan Stanley Trust                                          Morgan Stanley Services Company Inc.; Assistant Treasurer of
Harborside Financial Center,                                      Morgan Stanley Investment Advisors Inc., Morgan Stanley Services
Plaza Two,                                                        Company Inc. and Morgan Stanley Distributors Inc.; Vice President
Jersey City, NJ 07311                                             of the Retail Funds. Formerly, Treasurer of the Retail Funds
                                                                  (April 1989-July 2003).
</Table>

                                       18
<Page>

<Table>
<Caption>
                                                    TERM OF
                                  POSITION(S)      OFFICE AND
  NAME, AGE AND ADDRESS OF         HELD WITH       LENGTH OF
     EXECUTIVE OFFICER            REGISTRANT      TIME SERVED*              PRINCIPAL OCCUPATION(S) DURING PAST 5 YEARS**
- ------------------------------  --------------  ----------------  -----------------------------------------------------------------
                                                         
Mary E. Mullin (38)             Secretary       Since July 2003   Executive Director of Morgan Stanley & Co. Incorporated, Morgan
1221 Avenue of the Americas                                       Stanley Investment Advisors Inc. and Morgan Stanley Investment
New York, NY 10020                                                Management Inc. Secretary of the Retail Funds (since July 2003)
                                                                  and the Institutional Funds (since June 1999).
</Table>

- ----------
  *  THIS IS THE EARLIEST DATE THE OFFICER BEGAN SERVING THE RETAIL FUNDS. EACH
     OFFICER SERVES AN INDEFINITE TERM, UNTIL HIS OR HER SUCCESSOR IS ELECTED.
 **  THE DATES REFERENCED BELOW INDICATING COMMENCEMENT OF SERVICE AS AN OFFICER
     FOR THE RETAIL AND INSTITUTIONAL FUNDS REFLECT THE EARLIEST DATE THE
     OFFICER BEGAN SERVING THE RETAIL OR INSTITUTIONAL FUNDS, AS APPLICABLE.

                       2006 FEDERAL TAX NOTICE (UNAUDITED)

               Of the Fund's ordinary dividends paid during the fiscal
               year ended January 31, 2006, 50.91% was attributable to
               qualifying Federal obligations. Please consult your tax
               advisor to determine if any portion of the dividends
               you received is exempt from state income tax.

                                       19
<Page>

TRUSTEES
Michael Bozic
Charles A. Fiumefreddo
Edwin J. Garn
Wayne E. Hedien
James F. Higgins
Dr. Manuel H. Johnson
Joseph J. Kearns
Michael E. Nugent
Fergus Reid

OFFICERS
Charles A. Fiumefreddo
CHAIRMAN OF THE BOARD

Ronald E. Robison
PRESIDENT and PRINCIPAL EXECUTIVE OFFICER

J. David Germany
VICE PRESIDENT

Dennis F. Shea
VICE PRESIDENT

Barry Fink
VICE PRESIDENT

Amy R. Doberman
VICE PRESIDENT

Carsten Otto
CHIEF COMPLIANCE OFFICER

Stefanie V. Chang
VICE PRESIDENT

Francis J. Smith
TREASURER and CHIEF FINANCIAL OFFICER

Thomas F. Caloia
VICE PRESIDENT

Mary E. Mullin
SECRETARY

TRANSFER AGENT
Morgan Stanley Trust
Harborside Financial Center, Plaza Two
Jersey City, New Jersey 07311

INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM
Deloitte & Touche LLP
Two World Financial Center
New York, New York 10281

INVESTMENT ADVISER
Morgan Stanley Investment Advisors Inc.
1221 Avenue of the Americas
New York, New York 10020

This report is submitted for the general information of the shareholders of the
Fund. For more detailed information about the Fund, its fees and expenses and
other pertinent information, please read its Prospectus. The Fund's Statement of
Additional Information contains additional information about the Fund, including
its trustees. It is available, without charge, by calling (800) 869-NEWS.

This report is not authorized for distribution to prospective investors in the
Fund unless preceded or accompanied by an effective Prospectus. Read the
Prospectus carefully before investing.

Investments and services offered through Morgan Stanley DW Inc., member SIPC.
Morgan Stanley Distributors Inc., member NASD

(C) 2006 Morgan Stanley

[MORGAN STANLEY LOGO]

37960RPT-RA06-00215P-Y01/06

[GRAPHIC]
                                                            MORGAN STANLEY FUNDS

                                                                  MORGAN STANLEY
                                                                 U.S. GOVERNMENT
                                                              MONEY MARKET TRUST

                                                                   ANNUAL REPORT
                                                                JANUARY 31, 2006

[MORGAN STANLEY LOGO]
<Page>

Item 2.   Code of Ethics.

(a)     The Fund has adopted a code of ethics (the "Code of Ethics") that
applies to its principal executive officer, principal financial officer,
principal accounting officer or controller, or persons performing similar
functions, regardless of whether these individuals are employed by the Fund or a
third party.

(b)     No information need be disclosed pursuant to this paragraph.

(c)     The Fund has amended its Code of Ethics during the period covered by the
shareholder report presented in Item 1 hereto to delete from the end of the
following paragraph on page 2 of the Code the phrase "to the detriment of the
Fund.":

"Each Covered Officer must not use his personal influence or personal
relationship improperly to influence investment decisions or financial reporting
by the Fund whereby the Covered Officer would benefit personally (directly or
indirectly)."

Additionally, Exhibit B was amended to remove Mitchell M. Merin as a covered
officer.

(d)     Not applicable.

(e)     Not applicable.

(f)

        (1)    The Fund's Code of Ethics is attached hereto as Exhibit A.

        (2)    Not applicable.

        (3)    Not applicable.


Item 3.   Audit Committee Financial Expert.

The Fund's Board of Trustees has determined that it has two "audit committee
financial experts" serving on its audit committee, each of whom are
"independent" Trustees: Dr. Manuel H. Johnson and Joseph J. Kearns. Under
applicable securities laws, a person who is determined to be an audit committee
financial expert will not be deemed an "expert" for any purpose, including
without limitation for the purposes of Section 11 of the Securities Act of 1933,
as a result of being designated or identified as an audit committee financial
expert. The designation or identification of a person as an audit committee
financial expert does not impose on such person any duties, obligations, or
liabilities that are greater than the duties, obligations, and liabilities
imposed on such person as a member of the audit committee and Board of Trustees
in the absence of such designation or identification.

<Page>

                      MORGAN STANLEY U.S GOVT MONEY MARKET

Item 4.  Principal Accountant Fees and Services.

(a)(b)(c)(d) and (g).  Based on fees billed for the periods shown:

           2006
<Table>
Caption>
                                                            REGISTRANT            COVERED ENTITIES(1)
                                                                            
              AUDIT FEES                                    $ 25,768              N/A

              NON-AUDIT FEES
                  AUDIT-RELATED FEES                        $    540  (2)         $  5,190,300 (2)
                  TAX FEES                                  $  4,335  (3)         $  2,044,491 (4)
                  ALL OTHER FEES                            $      -              $         -
              TOTAL NON-AUDIT FEES                          $  4,875              $  7,234,791

              TOTAL                                         $ 30,643              $  7,234,791
</Table>

           2005
<Table>
Caption>
                                                            REGISTRANT            COVERED ENTITIES(1)
                                                                            
              AUDIT FEES                                    $ 23,689              N/A

              NON-AUDIT FEES
                  AUDIT-RELATED FEES                        $    684  (2)         $ 3,746,495  (2)
                  TAX FEES                                  $  4,757  (3)         $    79,800  (4)
                  ALL OTHER FEES                            $      -              $         -  (5)
              TOTAL NON-AUDIT FEES                          $  5,441              $ 3,826,295

              TOTAL                                         $ 29,130              $ 3,826,295
</Table>

              N/A- Not applicable, as not required by Item 4.

              (1) Covered Entities include the Adviser (excluding sub-advisors)
                  and any entity controlling, controlled by or under common
                  control with the Adviser that provides ongoing services to the
                  Registrant.
              (2) Audit-Related Fees represent assurance and related services
                  provided that are reasonably related to the performance of the
                  audit of the financial statements of the Covered Entities' and
                  funds advised by the Adviser or its affiliates, specifically
                  data verification and agreed-upon procedures related to asset
                  securitizations and agreed-upon procedures engagements.
              (3) Tax Fees represent tax compliance, tax planning and tax advice
                  services provided in connection with the preparation and
                  review of the Registrant's tax returns.
              (4) Tax Fees represent tax compliance, tax planning and tax advice
                  services provided in connection with the review of Covered
                  Entities' tax returns.
              (5) All other fees represent project management for future
                  business applications and improving business and operational
                  processes.

<Page>

(e)(1) The audit committee's pre-approval policies and procedures are as
follows:

                                                                      APPENDIX A

                                 AUDIT COMMITTEE
                          AUDIT AND NON-AUDIT SERVICES
                       PRE-APPROVAL POLICY AND PROCEDURES
                                     OF THE
                  MORGAN STANLEY RETAIL AND INSTITUTIONAL FUNDS

                     AS ADOPTED AND AMENDED JULY 23, 2004,(1)

     1.   STATEMENT OF PRINCIPLES

The Audit Committee of the Board is required to review and, in its sole
discretion, pre-approve all Covered Services to be provided by the Independent
Auditors to the Fund and Covered Entities in order to assure that services
performed by the Independent Auditors do not impair the auditor's independence
from the Fund.

The SEC has issued rules specifying the types of services that an independent
auditor may not provide to its audit client, as well as the audit committee's
administration of the engagement of the independent auditor. The SEC's rules
establish two different approaches to pre-approving services, which the SEC
considers to be equally valid. Proposed services either: may be pre-approved
without consideration of specific case-by-case services by the Audit Committee
("GENERAL PRE-APPROVAL"); or require the specific pre-approval of the Audit
Committee or its delegate ("SPECIFIC PRE-APPROVAL"). The Audit Committee
believes that the combination of these two approaches in this Policy will result
in an effective and efficient procedure to pre-approve services performed by the
Independent Auditors. As set forth in this Policy, unless a type of service has
received general pre-approval, it will require specific pre-approval by the
Audit Committee (or by any member of the Audit Committee to which pre-approval
authority has been delegated) if it is to be provided by the Independent
Auditors. Any proposed services exceeding pre-approved cost levels or budgeted
amounts will also require specific pre-approval by the Audit Committee.

The appendices to this Policy describe the Audit, Audit-related, Tax and All
Other services that have the general pre-approval of the Audit Committee. The
term of any general pre-approval is 12 months from the date of pre-approval,
unless the Audit Committee considers and provides a different period and states
otherwise. The Audit Committee will annually review and pre-approve the services
that may be provided by the Independent Auditors without obtaining specific
pre-approval from the Audit Committee. The Audit Committee will add to or
subtract from the list of general pre-approved services from time to time, based
on subsequent determinations.

- ----------
(1)      This Audit Committee Audit and Non-Audit Services Pre-Approval Policy
         and Procedures (the "POLICY"), adopted as of the date above, supersedes
         and replaces all prior versions that may have been adopted from time to
         time.

<Page>

The purpose of this Policy is to set forth the policy and procedures by which
the Audit Committee intends to fulfill its responsibilities. It does not
delegate the Audit Committee's responsibilities to pre-approve services
performed by the Independent Auditors to management.

The Fund's Independent Auditors have reviewed this Policy and believes that
implementation of the Policy will not adversely affect the Independent Auditors'
independence.

     2.   DELEGATION

As provided in the Act and the SEC's rules, the Audit Committee may delegate
either type of pre-approval authority to one or more of its members. The member
to whom such authority is delegated must report, for informational purposes
only, any pre-approval decisions to the Audit Committee at its next scheduled
meeting.

     3.   AUDIT SERVICES

The annual Audit services engagement terms and fees are subject to the specific
pre-approval of the Audit Committee. Audit services include the annual financial
statement audit and other procedures required to be performed by the Independent
Auditors to be able to form an opinion on the Fund's financial statements. These
other procedures include information systems and procedural reviews and testing
performed in order to understand and place reliance on the systems of internal
control, and consultations relating to the audit. The Audit Committee will
approve, if necessary, any changes in terms, conditions and fees resulting from
changes in audit scope, Fund structure or other items.

In addition to the annual Audit services engagement approved by the Audit
Committee, the Audit Committee may grant general pre-approval to other Audit
services, which are those services that only the Independent Auditors reasonably
can provide. Other Audit services may include statutory audits and services
associated with SEC registration statements (on Forms N-1A, N-2, N-3, N-4,
etc.), periodic reports and other documents filed with the SEC or other
documents issued in connection with securities offerings.

The Audit Committee has pre-approved the Audit services in Appendix B.1. All
other Audit services not listed in Appendix B.1 must be specifically
pre-approved by the Audit Committee (or by any member of the Audit Committee to
which pre-approval has been delegated).

     4.   AUDIT-RELATED SERVICES

Audit-related services are assurance and related services that are reasonably
related to the performance of the audit or review of the Fund's financial
statements and, to the extent they are Covered Services, the Covered Entities or
that are traditionally performed by the Independent Auditors. Because the Audit
Committee believes that the provision of Audit-related services does not impair
the independence of the auditor and is consistent with the SEC's rules on
auditor independence, the Audit Committee may grant general pre-approval to
Audit-related services. Audit-related services include, among others, accounting
consultations related to accounting, financial reporting or disclosure matters

<Page>

not classified as "Audit services"; assistance with understanding and
implementing new accounting and financial reporting guidance from rulemaking
authorities; agreed-upon or expanded audit procedures related to accounting
and/or billing records required to respond to or comply with financial,
accounting or regulatory reporting matters; and assistance with internal control
reporting requirements under Forms N-SAR and/or N-CSR.

The Audit Committee has pre-approved the Audit-related services in Appendix B.2.
All other Audit-related services not listed in Appendix B.2 must be specifically
pre-approved by the Audit Committee (or by any member of the Audit Committee to
which pre-approval has been delegated).

     5.   TAX SERVICES

The Audit Committee believes that the Independent Auditors can provide Tax
services to the Fund and, to the extent they are Covered Services, the Covered
Entities, such as tax compliance, tax planning and tax advice without impairing
the auditor's independence, and the SEC has stated that the Independent Auditors
may provide such services.

Pursuant to the preceding paragraph, the Audit Committee has pre-approved the
Tax Services in Appendix B.3. All Tax services in Appendix B.3 must be
specifically pre-approved by the Audit Committee (or by any member of the Audit
Committee to which pre-approval has been delegated).

     6.   ALL OTHER SERVICES

The Audit Committee believes, based on the SEC's rules prohibiting the
Independent Auditors from providing specific non-audit services, that other
types of non-audit services are permitted. Accordingly, the Audit Committee
believes it may grant general pre-approval to those permissible non-audit
services classified as All Other services that it believes are routine and
recurring services, would not impair the independence of the auditor and are
consistent with the SEC's rules on auditor independence.

The Audit Committee has pre-approved the All Other services in Appendix B.4.
Permissible All Other services not listed in Appendix B.4 must be specifically
pre-approved by the Audit Committee (or by any member of the Audit Committee to
which pre-approval has been delegated).

     7.   PRE-APPROVAL FEE LEVELS OR BUDGETED AMOUNTS

Pre-approval fee levels or budgeted amounts for all services to be provided by
the Independent Auditors will be established annually by the Audit Committee.
Any proposed services exceeding these levels or amounts will require specific
pre-approval by the Audit Committee. The Audit Committee is mindful of the
overall relationship of fees for audit and non-audit services in determining
whether to pre-approve any such services.

     8.   PROCEDURES

All requests or applications for services to be provided by the Independent
Auditors that do not require specific approval by the Audit Committee will be
submitted to the Fund's Chief Financial Officer and must include a detailed
description of the services to be

<Page>

rendered. The Fund's Chief Financial Officer will determine whether such
services are included within the list of services that have received the general
pre-approval of the Audit Committee. The Audit Committee will be informed on a
timely basis of any such services rendered by the Independent Auditors. Requests
or applications to provide services that require specific approval by the Audit
Committee will be submitted to the Audit Committee by both the Independent
Auditors and the Fund's Chief Financial Officer, and must include a joint
statement as to whether, in their view, the request or application is consistent
with the SEC's rules on auditor independence.

The Audit Committee has designated the Fund's Chief Financial Officer to monitor
the performance of all services provided by the Independent Auditors and to
determine whether such services are in compliance with this Policy. The Fund's
Chief Financial Officer will report to the Audit Committee on a periodic basis
on the results of its monitoring. Both the Fund's Chief Financial Officer and
management will immediately report to the chairman of the Audit Committee any
breach of this Policy that comes to the attention of the Fund's Chief Financial
Officer or any member of management.

     9.   ADDITIONAL REQUIREMENTS

The Audit Committee has determined to take additional measures on an annual
basis to meet its responsibility to oversee the work of the Independent Auditors
and to assure the auditor's independence from the Fund, such as reviewing a
formal written statement from the Independent Auditors delineating all
relationships between the Independent Auditors and the Fund, consistent with
Independence Standards Board No. 1, and discussing with the Independent Auditors
its methods and procedures for ensuring independence.

     10.  COVERED ENTITIES

Covered Entities include the Fund's investment adviser(s) and any entity
controlling, controlled by or under common control with the Fund's investment
adviser(s) that provides ongoing services to the Fund(s). Beginning with
non-audit service contracts entered into on or after May 6, 2003, the Fund's
audit committee must pre-approve non-audit services provided not only to the
Fund but also to the Covered Entities if the engagements relate directly to the
operations and financial reporting of the Fund. This list of Covered Entities
would include:

          MORGAN STANLEY RETAIL FUNDS
          Morgan Stanley Investment Advisors Inc.
          Morgan Stanley & Co. Incorporated
          Morgan Stanley DW Inc.
          Morgan Stanley Investment Management Inc.
          Morgan Stanley Investment Management Limited
          Morgan Stanley Investment Management Private Limited
          Morgan Stanley Asset & Investment Trust Management Co., Limited
          Morgan Stanley Investment Management Company
          Van Kampen Asset Management
          Morgan Stanley Services Company, Inc.
          Morgan Stanley Distributors Inc.
          Morgan Stanley Trust FSB

<Page>

          MORGAN STANLEY INSTITUTIONAL FUNDS
          Morgan Stanley Investment Management Inc.
          Morgan Stanley Investment Advisors Inc.
          Morgan Stanley Investment Management Limited
          Morgan Stanley Investment Management Private Limited
          Morgan Stanley Asset & Investment Trust Management Co., Limited
          Morgan Stanley Investment Management Company
          Morgan Stanley & Co. Incorporated
          Morgan Stanley Distribution, Inc.
          Morgan Stanley AIP GP LP
          Morgan Stanley Alternative Investment Partners LP

(e)(2) Beginning with non-audit service contracts entered into on or after May
6, 2003, the audit committee also is required to pre-approve services to Covered
Entities to the extent that the services are determined to have a direct impact
on the operations or financial reporting of the Registrant. 100% of such
services were pre-approved by the audit committee pursuant to the Audit
Committee's pre-approval policies and procedures (attached hereto).

(f)      Not applicable.

(g)      See table above.

(h)      The audit committee of the Board of Trustees has considered whether the
provision of services other than audit services performed by the auditors to the
Registrant and Covered Entities is compatible with maintaining the auditors'
independence in performing audit services.

Item 5.   Audit Committee of Listed Registrants.

(a)  The Fund has a separately-designated standing audit committee established
in accordance with Section 3(a)(58)(A) of the Exchange Act whose members are:
Michael Bozic, Edwin J. Garn, Wayne E. Hedien, Manual H. Johnson, Joseph J.
Kearns, Michael Nugent and Fergus Reid.

(b)  Not applicable.

Item 6.   Schedule of Investments

Refer to Item 1.

<Page>

Item 7.   Disclosure of Proxy Voting Policies and Procedures for Closed-End
Management Investment Companies.

Applicable only to reports filed by closed-end funds.

Item 8.   Portfolio Managers of Closed-End Management Investment Companies

Applicable only to reports filed by closed-end funds.


Item 9.   Closed-End Fund Repurchases

Applicable only to reports filed by closed-end funds.

Item 10.  Submission of Matters to a Vote of Security Holders

Not applicable.

Item 11.  Controls and Procedures

(a)  The Fund's principal executive officer and principal financial officer have
concluded that the Fund's disclosure controls and procedures are sufficient to
ensure that information required to be disclosed by the Fund in this Form N-CSR
was recorded, processed, summarized and reported within the time periods
specified in the Securities and Exchange Commission's rules and forms, based
upon such officers' evaluation of these controls and procedures as of a date
within 90 days of the filing date of the report.

(b)  There were no changes in the registrant's internal control over financial
reporting that occurred during the registrant's most recent fiscal half-year
(the registrant's second fiscal half-year in the case of an annual report) that
has materially affected, or is reasonably likely to materially affect, the
registrant's internal control over financial reporting.

Item 12.  Exhibits

(a)  The Code of Ethics for Principal Executive and Senior Financial Officers is
attached hereto.

(b)  A separate certification for each principal executive officer and principal
financial officer of the registrant are attached hereto as part of EX-99.CERT.
<Page>

                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.

Morgan Stanley U.S. Government Money Market Trust

/s/ Ronald E. Robison
Ronald E. Robison
Principal Executive Officer
March 23, 2006

     Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed by the following
persons on behalf of the registrant and in the capacities and on the dates
indicated.

/s/ Ronald E. Robison
Ronald E. Robison
Principal Executive Officer
March 23, 2006

/s/ Francis Smith
Francis Smith
Principal Financial Officer
March 23, 2006