                                                                    Exhibit 32.1

                            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 the Quarterly Report of Phase III Medical, Inc. (the
"Company") on Form 10-Q for the period ended June 30, 2004 filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Mark
Weinreb, Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C.
Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of
2002, that:

     (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 of the Company as of the
          dates presented and the result of operations of the Company for the
          periods presented.

Dated:  August 13, 2004



                                                 /s/Mark Weinreb
                                                 -----------------------
                                                 Mark Weinreb
                                                 Chief Executive Officer

The foregoing certification is being furnished solely pursuant to Section
906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350,
Chapter 63 of Title 18, United States Code) and is not being filed as part of
the Form 10-Q or as a separate disclosure document.

A signed original of this written statement required by Section 906 has
been provided to Phase III Medical, Inc. and will be retained by Phase III
Medical, Inc. and furnished to the Securities and Exchange Commission or its
staff upon request.








