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

Robert L. Parkinson, Jr., as Chairman of the Board and Chief Executive Officer of Baxter International Inc. (the “Company”), certifies, pursuant to 18 U.S.C. §1350, as adopted pursuant to §906 of the Sarbanes-Oxley Act of 2002, that:

(1) the Company’s Quarterly Report on Form 10-Q for the quarterly period ended March 31, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”) fully complies with the requirements of Section 13(a) 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.

/s/ Robert L. Parkinson, Jr.

Robert L. Parkinson, Jr.

Chairman of the Board and Chief Executive Officer

May 10, 2004