<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, 2005

Date of reporting period: January 31, 2005


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 THE FUND WILL ACHIEVE ITS INVESTMENT OBJECTIVE.
THE FUND IS SUBJECT TO MARKET RISK, WHICH IS THE POSSIBILITY THAT MARKET VALUES
OF SECURITIES OWNED BY THE FUND WILL DECLINE AND, THEREFORE, THE VALUE OF THE
FUND'S SHARES MAY BE LESS THAN WHAT YOU PAID FOR THEM. ACCORDINGLY, YOU CAN LOSE
MONEY INVESTING IN THIS FUND.

<Page>

FUND REPORT

For the year ended January 31, 2005

MARKET CONDITIONS

During the 12 months ended January 31, 2005, favorable economic trends began to
appear. While the growth of the gross domestic product (or GDP) fell somewhat in
the fourth quarter of 2004 to 3.1 percent, it had been above this level for the
three previous quarters of the year. Job growth (as measured by non-farm
payrolls), which slowed in mid 2004, appeared to regain some momentum after
July. In addition, leading economic indicators turned positive in November,
after posting five consecutive months of contraction. As a result, January 2005
consumer confidence rose to its highest level in six months, well above
analysts' expectations.

The Federal Open Market Committee (the "Fed") began its current tightening cycle
at its June 30 meeting, and went on to increase its target rate for federal
funds a cumulative 125 basis points over five separate meetings to 2.25 percent
as of the December meeting. The Fed's formal risk assessment was balanced, and
they have stated that increases will continue at a "measured pace." Against this
backdrop, money market fund yield levels began to rise from record lows.

PERFORMANCE ANALYSIS

As of January 31, 2005, the U.S. Government Money Market Trust had net assets in
excess of $1.12 billion. For the 12-month period ended January 31, 2005, the
Fund provided a return of 0.78 percent. For the seven-day period ended January
31, 2005, the Fund provided an effective annualized yield of 1.68 percent and a
current annualized yield of 1.66 percent, while its 30-day moving average
annualized yield for January was 1.64 percent.
PAST PERFORMANCE IS NO GUARANTEE OF FUTURE RESULTS.

Our strategy in managing the Fund remained consistent with our long-term focus
on maintaining preservation of capital and liquidity. On January 31, 2005,
approximately 57 percent of the Fund was invested in Federal Home Loan Bank
obligations, 19 percent in Federal Home Loan Mortgage Corporation obligations,
11 percent in repurchase agreements, 10 percent in Federal National Mortgage
Association obligations, two percent in Federal Farm Credit Bank obligations and
one percent in direct Treasuries. As of the end of January, the Fund's weighted
average maturity was 36 days and 95 percent of holdings were due to mature
within three months.

THERE IS NO GUARANTEE THAT ANY SECTORS MENTIONED WILL CONTINUE TO PERFORM WELL
OR BE HELD BY THE FUND IN THE FUTURE.

PORTFOLIO COMPOSITION

<Table>
                                                        
U.S. Government Agencies                                   88.3%
Repurchase Agreements                                      11.1
U.S. Treasury Bills                                         0.6
</Table>

MATURITY SCHEDULE

<Table>
                                                        
  1 - 30 Days                                              53.8%
 31 - 60 Days                                              24.2
 61 - 90 Days                                              17.2
 91 - 120 Days                                              2.9
121+ Days                                                   1.9
</Table>

DATA AS OF JANUARY 31, 2005. SUBJECT TO CHANGE DAILY. ALL PERCENTAGES FOR
PORTFOLIO COMPOSITION AND MATURITY SCHEDULE ARE AS A PERCENTAGE OF TOTAL
INVESTMENTS. PROVIDED FOR INFORMATIONAL PURPOSES ONLY AND SHOULD NOT BE DEEMED A
RECOMMENDATION TO BUY OR SELL THE SECURITIES MENTIONED. MORGAN STANLEY IS A
FULL-SERVICE SECURITIES FIRM ENGAGED IN SECURITIES TRADING AND BROKERAGE
ACTIVITIES, INVESTMENT BANKING, RESEARCH AND ANALYSIS, FINANCING AND FINANCIAL
ADVISORY SERVICES.

                                        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. YOU MAY OBTAIN COPIES OF A FUND'S FISCAL
QUARTER FILINGS BY CONTACTING MORGAN STANLEY CLIENT RELATIONS AT (800) 869-NEWS.

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 management
fees; distribution and service (12b-1) fees; 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 of 08/01/04 - 01/31/05.

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 *
                                                          ---------------   ---------------   ---------------
                                                                                                  08/01/04 -
                                                              08/01/04          01/31/05          01/31/05
                                                          ---------------   ---------------   ---------------
                                                                                     
Actual (0.59% return)                                     $      1,000.00   $      1,005.90   $          3.68
Hypothetical (5% annual return before expenses)           $      1,000.00   $      1,021.47   $          3.71
</Table>

- ----------
  *  EXPENSES ARE EQUAL TO THE FUND'S ANNUALIZED EXPENSE RATIO OF 0.73%
     MULTIPLIED BY THE AVERAGE ACCOUNT VALUE OVER THE PERIOD, MULTIPLIED BY
     184/366 (TO REFLECT THE ONE-HALF YEAR PERIOD).

                                        4
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST

PORTFOLIO OF INVESTMENTS - JANUARY 31, 2005

<Table>
<Caption>
                                                              ANNUALIZED
   PRINCIPAL                                                    YIELD
   AMOUNT IN                                                  ON DATE OF        MATURITY
   THOUSANDS     DESCRIPTION                                   PURCHASE           DATE                 VALUE
- -------------------------------------------------------------------------------------------------------------------
                                                                                      
                 U.S. GOVERNMENT AGENCY - DISCOUNT NOTES (63.2%)
$       384,447  Federal Home Loan Banks                     2.06 - 2.65%   02/02/05 - 06/17/05   $     383,491,168
        214,803  Federal Home Loan Mortgage Corp.            1.93 - 2.55    02/03/05 - 05/31/05         214,076,358
        112,311  Federal National Mortgage Assoc.            1.93 - 2.60    02/02/05 - 04/27/05         112,087,347
                                                                                                  -----------------
                 TOTAL U.S. GOVERNMENT AGENCY - DISCOUNT NOTES
                   (COST $709,654,873)                                                                  709,654,873
                                                                                                  -----------------
                 U.S. GOVERNMENT AGENCY - FLOATING RATE NOTES (25.9%)
         25,000  Federal Farm Credit Banks                       2.42             04/21/05               24,998,918
        265,000  Federal Home Loan Banks                     2.28 - 2.48    03/15/05 - 09/16/05         264,980,973
                                                                                                  -----------------
                 TOTAL U.S. GOVERNMENT AGENCY - FLOATING RATE NOTES
                   (COST $289,979,891)                                                                  289,979,891
                                                                                                  -----------------
                 REPURCHASE AGREEMENTS (11.2%)
        104,500  Banc of America Securities LLC (dated
                   01/31/05; proceeds $104,507,257) (a)           2.50            02/01/05              104,500,000
         20,000  Goldman Sachs Group, Inc. (The) (dated
                   01/27/05; proceeds $20,018,744) (b)            2.41            02/10/05               20,000,000
          1,393  The Bank of New York (dated 01/31/05;
                   proceeds $1,393,194) (c)                      2.375            02/01/05                1,393,102
                                                                                                  -----------------
                 TOTAL REPURCHASE AGREEMENTS
                   (COST $125,893,102)                                                                  125,893,102
                                                                                                  -----------------
                 U.S. GOVERNMENT OBLIGATION (0.6%)
          7,000  U.S. Treasury Bill
                   (COST $6,927,280)                             2.54             06/30/05                6,927,280
                                                                                                  -----------------
                 TOTAL INVESTMENTS
                   (COST $1,132,455,146) (d)                                       100.9%             1,132,455,146
                 LIABILITIES IN EXCESS OF OTHER ASSETS                              (0.9)                (9,709,397)
                                                                                   -----          -----------------
                 NET ASSETS                                                        100.0%         $   1,122,745,749
                                                                                   =====          =================
</Table>

- ----------
   (a)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 5.00% DUE 10/01/33
        VALUED AT $48,823,268 AND FEDERAL MORTGAGE ACCEPTANCE CORP. 4.50% DUE
        06/01/19 VALUED AT $57,766,732.
   (b)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 0.00% DUE 03/16/05
        VALUED AT $20,400,614.
   (c)  COLLATERALIZED BY FEDERAL NATIONAL MORTGAGE ASSOC. 4.187% DUE 03/01/34
        VALUED AT $1,420,964.
   (d)  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, 2005

<Table>
                                                                                     
ASSETS:
Investments in securities, at value (cost $1,132,455,146)
  (including repurchase agreements of $125,893,102)                                     $   1,132,455,146
Cash                                                                                               90,001
Receivable for:
  Interest                                                                                        631,177
  Shares of beneficial interest sold                                                               11,060
Prepaid expenses and other assets                                                                  66,133
                                                                                        -----------------
    TOTAL ASSETS                                                                            1,133,253,517
                                                                                        -----------------
LIABILITIES:
Payable for:
  Shares of beneficial interest redeemed                                                        9,838,379
  Investment advisory fee                                                                         374,325
  Distribution fee                                                                                 77,584
  Administration fee                                                                               48,271
Accrued expenses and other payables                                                               169,209
                                                                                        -----------------
    TOTAL LIABILITIES                                                                          10,507,768
                                                                                        -----------------
    NET ASSETS                                                                          $   1,122,745,749
                                                                                        =================
COMPOSITION OF NET ASSETS:
Paid-in-capital                                                                         $   1,122,660,636
Accumulated undistributed net investment income                                                    85,113
                                                                                        -----------------
    NET ASSETS                                                                          $   1,122,745,749
                                                                                        =================
NET ASSET VALUE PER SHARE,
  1,122,725,548 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, 2005

<Table>
                                                                                     
NET INVESTMENT INCOME:

INTEREST INCOME                                                                         $      17,725,042
                                                                                        -----------------
EXPENSES
Investment advisory fee                                                                         5,086,337
Transfer agent fees and expenses                                                                1,870,332
Distribution fee                                                                                1,188,929
Shareholder reports and notices                                                                   210,841
Administration fee                                                                                144,007
Registration fees                                                                                  78,579
Professional fees                                                                                  67,509
Custodian fees                                                                                     59,666
Trustees' fees and expenses                                                                        24,566
Other                                                                                              52,947
                                                                                        -----------------
    TOTAL EXPENSES                                                                              8,783,713
                                                                                        -----------------
NET INVESTMENT INCOME                                                                   $       8,941,329
                                                                                        =================
</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, 2005     JANUARY 31, 2004
                                                                         ------------------    ------------------
                                                                                         
INCREASE (DECREASE) IN NET ASSETS:
OPERATIONS:
Net investment income                                                    $        8,941,329    $        5,655,210

Dividends to shareholders from net investment income                             (8,966,340)           (5,677,194)

Net decrease from transactions in shares of beneficial interest                (146,513,383)          (70,286,719)
                                                                         ------------------    ------------------

    NET DECREASE                                                               (146,538,394)          (70,308,703)

NET ASSETS:
Beginning of period                                                           1,269,284,143         1,339,592,846
                                                                         ------------------    ------------------

END OF PERIOD
(INCLUDING ACCUMULATED UNDISTRIBUTED NET INVESTMENT INCOME OF
$85,113 AND $110,124, RESPECTIVELY)                                      $    1,122,745,749    $    1,269,284,143
                                                                         ==================    ==================
</Table>

                        SEE NOTES TO FINANCIAL STATEMENTS

                                        8
<Page>

MORGAN STANLEY U.S. GOVERNMENT MONEY MARKET TRUST

NOTES TO FINANCIAL STATEMENTS - JANUARY 31, 2005

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.

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
Effective November 1, 2004, 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

                                        9

<Page>

exceeding $1.5 billion; 0.275% to the 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.

Effective November 1, 2004, 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.

Prior to November 1, 2004, the Fund had retained the Investment Adviser to
provide administrative services and to manage the investment of the Fund's
assets pursuant to an investment management agreement pursuant to which the Fund
paid the Investment Adviser a monthly management 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: 0.50% to the portion of the
daily net assets not exceeding $500 million; 0.425% to the portion of the daily
net assets exceeding $500 million but not exceeding $750 million; 0.375% to the
portion of the daily net assets exceeding $750 million but not exceeding $1
billion; 0.35% to the portion of the daily net assets exceeding $1 billion but
not exceeding $1.5 billion; 0.325% to the portion of the daily net assets
exceeding $1.5 billion but not exceeding $2 billion; 0.30% to the portion of the
daily net assets exceeding $2 billion but not exceeding $2.5 billion; 0.275% to
the portion of the daily net assets exceeding $2.5 billion but not exceeding $3
billion; and 0.25% to the portion of the daily net assets exceeding $3 billion.

For the year ended January 31, 2005 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, 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, 2005, the distribution
fee was accrued at the annual rate of 0.10%.

                                       10
<Page>

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, 2005 aggregated $26,343,738,180 and
$26,503,766,156, respectively.

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.
Aggregate pension costs for the year ended January 31, 2005 included in
Trustees' fees and expenses in the Statement of Operations amounted to $7,417.
At January 31, 2005, the Fund had an accrued pension liability of $60,952 which
is included in accrued expenses in the Statement of Assets and Liabilities. On
December 2, 2003, 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.

Effective April 1, 2004, the Fund began 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, 2005    JANUARY 31, 2004
                                                                ----------------    ----------------
                                                                                
Shares sold                                                        2,729,300,423       3,002,675,253
Shares issued in reinvestment of dividends                             8,935,675           5,661,041
                                                                ----------------    ----------------
                                                                   2,738,236,098       3,008,336,294
Shares redeemed                                                   (2,884,749,481)     (3,078,623,013)
                                                                ----------------    ----------------
Net decrease                                                        (146,513,383)        (70,286,719)
                                                                ================    ================
</Table>

                                       11
<Page>

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 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 10, 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 early stage of the litigation, and no provision has been made in the Fund's
financial statements for the effect, if any, of this matter.

                                       12
<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,
                                         -----------------------------------------------------------------------------------------
                                             2005             2004                2003                2002                2001
                                         ------------     ------------        ------------        ------------        ------------
                                                                                                       
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                                     0.008            0.004               0.011               0.032               0.056
Less dividends from net investment
 income                                        (0.008)          (0.004)             (0.011)             (0.032)             (0.056)
                                         ------------     ------------        ------------        ------------        ------------

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

TOTAL RETURN                                     0.78%            0.45%               1.06%               3.25%               5.80%

RATIOS TO AVERAGE NET ASSETS:
Expenses                                         0.73%            0.71%(1)            0.74%(1)            0.74%(1)            0.78%
Net investment income                            0.74%            0.43%(1)            1.03%(1)            3.14%(1)            5.61%

SUPPLEMENTAL DATA:
Net assets, end of period, in millions   $      1,123     $      1,269        $      1,340        $      1,257        $      1,243
</Table>

- ----------
(1)  IF THE FUND HAD BORNE ALL ITS EXPENSES THAT WERE REIMBURSED OR WAIVED BY
     THE INVESTMENT ADVISER, 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, 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

                                       13
<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, 2005, 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 controls over financial reporting. Our audit 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, 2005, by correspondence with the custodian
and brokers. 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, 2005, 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 15, 2005

                                       14
<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 (64)                      Trustee     Since        Private Investor; Director or  208           None.
c/o Kramer Levin Naftalis & Frankel LLP             April 1994   Trustee of the Retail Funds
Counsel to the Independent Trustees                              (since April 1994) and the
919 Third Avenue                                                 Institutional Funds (since
New York, NY 10022-3902                                          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 (72)                      Trustee     Since        Consultant; Managing Director  208           Director of Franklin
1031 N. Chartwell Court                             January 1993 of Summit Ventures LLC;                      Covey (time
Salt Lake City, UT 84103                                         Director or Trustee of the                   management systems),
                                                                 Retail Funds (since January                  BMW Bank of North
                                                                 1993) and the Institutional                  America, Inc.
                                                                 Funds (since July 2003);                     (industrial loan
                                                                 member of the Utah Regional                  corporation), United
                                                                 Advisory Board of Pacific                    Space Alliance (joint
                                                                 Corp.; formerly Managing                     venture between
                                                                 Director of Summit Ventures                  Lockheed Martin and
                                                                 LLC (2000-2004); United States               the Boeing Company)
                                                                 Senator (R-Utah) (1974-1992)                 and Nuskin Asia
                                                                 and Chairman, Senate Banking                 Pacific (multilevel
                                                                 Committee (1980-1986), Mayor                 marketing); member of
                                                                 of Salt Lake City, Utah                      the board of various
                                                                 (1971-1974), Astronaut, Space                civic and charitable
                                                                 Shuttle Discovery (April                     organizations.
                                                                 12-19, 1985), and Vice
                                                                 Chairman, Huntsman Corporation
                                                                 (chemical company).

Wayne E. Hedien (70)                    Trustee     Since        Retired; Director or Trustee   208           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);
919 Third Avenue                                                 Institutional Funds (since                   Trustee and Vice
New York, NY 10022-3902                                          July 2003); formerly                         Chairman of The Field
                                                                 associated with the Allstate                 Museum of Natural
                                                                 Companies (1966-1994), most                  History; director of
                                                                 recently as Chairman of The                  various other
                                                                 Allstate Corporation (March                  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>

                                       15
<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 (55)              Trustee     Since        Senior Partner, Johnson Smick  208           Director of NVR, Inc.
c/o Johnson Smick International, Inc.               July 1991    International, Inc., a                       (home construction);
2099 Pennsylvania Avenue, N.W.                                   consulting firm; Chairman of                 Director of KFX
Suite 950                                                        the Audit Committee and                      Energy; Director of
Washington, D.C. 20006                                           Director or Trustee of the                   RBS Greenwich Capital
                                                                 Retail Funds (since July 1991)               Holdings (financial
                                                                 and the Institutional Funds                  holding company).
                                                                 (since July 2003); Co-Chairman
                                                                 and a founder of 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 (62)                   Trustee     Since        President, Kearns & Associates 209           Director of Electro
c/o Kearns & Associates LLC                         July 2003    LLC (investment consulting);                 Rent Corporation
PMB754                                                           Deputy Chairman of the Audit                 (equipment leasing),
23852 Pacific Coast Highway                                      Committee and Director or                    The Ford Family
Malibu, CA 90265                                                 Trustee of the Retail Funds                  Foundation, and the
                                                                 (since July 2003) and the                    UCLA Foundation.
                                                                 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 (68)                  Trustee     Since        General Partner of Triumph     208           Director of various
c/o Triumph Capital, L.P.                           July 1991    Capital, L.P., a private                     business
445 Park Avenue                                                  investment partnership;                      organizations.
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 (72)                        Trustee     Since        Chairman of Lumelite Plastics  209           Trustee and Director
c/o Lumelite Plastics Corporation                   July 2003    Corporation; Chairman of the                 of certain investment
85 Charles Colman Blvd.                                          Governance Committee and                     companies in the
Pawling, NY 12564                                                Director or Trustee of the                   JPMorgan Funds
                                                                 Retail Funds (since July 2003)               complex managed by
                                                                 and the Institutional Funds                  J.P. Morgan
                                                                 (since June 1992).                           Investment Management
                                                                                                              Inc.
</Table>

                                       16
<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 (71)             Chairman of Since        Chairman and Director or       208           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 (56)                   Trustee     Since        Director or Trustee of the     208           Director of AXA
c/o Morgan Stanley Trust                            June 2000    Retail Funds (since June 2000)               Financial, Inc. and
Harborside Financial Center,                                     and the Institutional Funds                  The Equitable Life
Plaza Two,                                                       (since July 2003); Senior                    Assurance Society of
Jersey City, NJ 07311                                            Advisor of Morgan Stanley                    the United States
                                                                 (since August 2000); Director                (financial services).
                                                                 of the Distributor and Dean
                                                                 Witter Realty Inc.; previously
                                                                 President and Chief Operating
                                                                 Officer of the Private Client
                                                                 Group of Morgan Stanley (May
                                                                 1999-August 2000), and
                                                                 President and Chief Operating
                                                                 Officer of Individual
                                                                 Securities of Morgan Stanley
                                                                 (February 1997-May 1999).
</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.).

                                       17
<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**
- -----------------------------  --------------- ----------------  -------------------------------------------------------------
                                                        
Mitchell M. Merin (51)         President        Since May 1999   President and Chief Operating Officer of Morgan Stanley
1221 Avenue of the Americas                                      Investment Management Inc.; President, Director and Chief
New York, NY 10020                                               Executive Officer of the Investment Adviser and the
                                                                 Administrator; Chairman and Director of the Distributor;
                                                                 Chairman and Director of the Transfer Agent; Director of
                                                                 various Morgan Stanley subsidiaries; President of the
                                                                 Institutional Funds (since July 2003) and President of the
                                                                 Retail Funds; Trustee (since July 2003) and President (since
                                                                 December 2002) of the Van Kampen Closed-End Funds; Trustee
                                                                 and President (since October 2002) of the Van Kampen Open-End
                                                                 Funds.

Ronald E. Robison (66)         Executive Vice   Since            Principal Executive Officer of Funds in the Fund Complex
1221 Avenue of the Americas    President and    April 2003       (since May 2003); Managing Director of Morgan Stanley & Co.
New York, NY 10020             Principal                         Incorporated, Morgan Stanley Investment Management Inc. and
                               Executive                         Morgan Stanley; Managing Director, Chief Administrative
                               Officer                           Officer and Director of the Investment Adviser and the
                                                                 Administrator; Director of the Transfer Agent; Managing
                                                                 Director and Director of the Distributor; Executive Vice
                                                                 President and Principal Executive Officer of the
                                                                 Institutional Funds (since July 2003) and the Retail Funds
                                                                 (since April 2003); Director of Morgan Stanley SICAV (since
                                                                 May 2004); previously President and Director of the Retail
                                                                 Funds (March 2001-July 2003) and Chief Global Operations
                                                                 Officer and Managing Director of Morgan Stanley Investment
                                                                 Management Inc.

Joseph J. McAlinden (62)       Vice President   Since July 1995  Managing Director and Chief Investment Officer of the
1221 Avenue of the Americas                                      Investment Adviser and Morgan Stanley Investment Management
New York, NY 10020                                               Inc., Director of the Transfer Agent, Chief Investment
                                                                 Officer of the Van Kampen Funds; Vice President of the
                                                                 Institutional Funds (since July 2003) and the Retail Funds
                                                                 (since July 1995).

Barry Fink (50)                Vice President   Since            General Counsel (since May 2000) and Managing Director (since
1221 Avenue of the Americas                     February 1997    December 2000) of Morgan Stanley Investment Management;
New York, NY 10020                                               Managing Director (since December 2000), Secretary (since
                                                                 February 1997) and Director of the Investment Adviser and the
                                                                 Administrator; Vice President of the Retail Funds; Assistant
                                                                 Secretary of Morgan Stanley DW; Vice President of the
                                                                 Institutional Funds (since July 2003); Managing Director,
                                                                 Secretary and Director of the Distributor; previously
                                                                 Secretary (February 1997-July 2003) and General Counsel
                                                                 (February 1997-April 2004) of the Retail Funds; Vice
                                                                 President and Assistant General Counsel of the Investment
                                                                 Adviser and the Administrator (February 1997-December 2001).

Amy R. Doberman (42)           Vice President   Since July 2004  Managing Director and General Counsel, U.S. Investment
1221 Avenue of the Americas                                      Management; Managing Director of Morgan Stanley Investment
New York, NY 10020                                               Management Inc. and the Investment Adviser, Vice President of
                                                                 the Institutional and Retail Funds (since July 2004); Vice
                                                                 President of the Van Kampen Funds (since August 2004);
                                                                 previously, Managing Director and General Counsel - Americas,
                                                                 UBS Global Asset Management (July 2000 - July 2004) and
                                                                 General Counsel, Aeltus Investment Management, Inc. (January
                                                                 1997 - July 2000).

Carsten Otto (41)              Chief            Since October    Executive Director and U.S. Director of Compliance for Morgan
1221 Avenue of the Americas    Compliance       2004             Stanley Investment Management (since October 2004); Executive
New York, NY 10020             Officer                           Director of the Investment Adviser and Morgan Stanley
                                                                 Investment Management Inc.; formerly Assistant Secretary and
                                                                 Assistant General Counsel of the Morgan Stanley Retail Funds.
</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**
- -----------------------------  --------------- ----------------  -------------------------------------------------------------
                                                        
Stefanie V. Chang (38)         Vice President   Since July 2003  Executive Director of Morgan Stanley & Co. Incorporated,
1221 Avenue of the Americas                                      Morgan Stanley Investment Management Inc., and the Investment
New York, NY 10020                                               Adviser; Vice President of the Institutional Funds and the
                                                                 Retail Funds (since July 2003); formerly practiced law with
                                                                 the New York law firm of Rogers & Wells (now Clifford Chance
                                                                 US LLP).

Francis J. Smith (39)          Treasurer and    Treasurer since  Executive Director of the Investment Adviser and Morgan
c/o Morgan Stanley Trust       Chief Financial  July 2003 and    Stanley Services (since December 2001); previously, Vice
Harborside Financial Center,   Officer          Chief Financial  President of the Retail Funds (September 2002-July 2003), and
Plaza Two,                                      Officer since    Vice President of the Investment Adviser and the
Jersey City, NJ 07311                           September 2002   Administrator (August 2000-November 2001) and Senior Manager
                                                                 at PricewaterhouseCoopers LLP (January 1998-August 2000).

Thomas F. Caloia (58)          Vice President   Since July 2003  Executive Director (since December 2002) and Assistant
c/o Morgan Stanley Trust                                         Treasurer of the Investment Adviser, the Distributor and the
Harborside Financial Center,                                     Administrator; previously Treasurer of the Retail Funds
Plaza Two,                                                       (April 1989-July 2003); formerly First Vice President of the
Jersey City, NJ 07311                                            Investment Adviser, the Distributor and the Administrator.

Mary E. Mullin (37)            Secretary        Since July 2003  Executive Director of Morgan Stanley & Co. Incorporated,
1221 Avenue of the Americas                                      Morgan Stanley Investment Management Inc. and the Investment
New York, NY 10020                                               Adviser; Secretary of the Institutional Funds and the Retail
                                                                 Funds (since July 2003); formerly practiced law with the New
                                                                 York law firms of McDermott, Will & Emery and Skadden, Arps,
                                                                 Slate, Meagher & Flom LLP.
</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.

                       2005 FEDERAL TAX NOTICE (UNAUDITED)

          Of the Fund's ordinary income dividends paid during the fiscal year
          ended January 31, 2005, 52.80% 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

Mitchell M. Merin
PRESIDENT

Ronald E. Robison
EXECUTIVE VICE PRESIDENT AND PRINCIPAL EXECUTIVE OFFICER

Joseph J. McAlinden
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) 2005 Morgan Stanley

[MORGAN STANLEY LOGO]

37965RPT-RA05-00182P-Y01/05

[GRAPHIC]
                                                            MORGAN STANLEY FUNDS


                                                                  MORGAN STANLEY
                                                                 U.S. GOVERNMENT
                                                              MONEY MARKET TRUST


                                                                   ANNUAL REPORT
                                                                JANUARY 31, 2005


[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)."

(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>

Item 4.  Principal Accountant Fees and Services.

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

       2005

<Table>
<Caption>
                                                                          REGISTRANT       COVERED ENTITIES(1)
                                                                                     
          AUDIT FEES                                                     $     24,546                  N/A

          NON-AUDIT FEES
               AUDIT-RELATED FEES                                        $        452(2)   $     3,746,495(2)
               TAX FEES                                                  $      4,877(3)   $        79,800(4)
               ALL OTHER FEES                                            $          -      $             -
          TOTAL NON-AUDIT FEES                                           $      5,329      $     3,826,295

          TOTAL                                                          $     29,875      $     3,826,295
</Table>

       2004

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

          NON-AUDIT FEES

               AUDIT-RELATED FEES                                        $        684(2)   $     2,847,161(2)
               TAX FEES                                                  $      4,757(3)   $       736,810(4)
               ALL OTHER FEES                                            $          -      $             -(5)
          TOTAL NON-AUDIT FEES                                           $      5,441      $     3,583,971

          TOTAL                                                          $     29,130      $     3,583,971
</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.

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(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 22, 2005

     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 22, 2005

/s/ Francis Smith
Francis Smith
Principal Financial Officer
March 22, 2005