EXHIBIT 13.(A).1.

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with this Amendment No. 1 to Annual Report of Tefron Ltd.
(the "Company") on Form 20-F/A for the period ending December 31, 2003, as filed
with the Securities and Exchange Commission on the date hereof (the Form 20-F,
as amended, called the "Report"), the undersigned hereby certify that to the
best of our knowledge:

     1. The Report fully complies with the requirements of Section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

     2. The information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

Date: September 21, 2004                             /s/ Yosef Shiran
                                                     -----------------------
                                                     Yosef Shiran
                                                     Chief Executive Officer


Date: September 21, 2004                             /s/ Gil Rozen
                                                     -----------------------
                                                     Gil Rozen
                                                     Chief Financial Officer