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 March 31, 2005 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: May 16, 2005


                                                         /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.