Exhibit 32.1

CHIEF EXECUTIVE OFFICER

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 Annual Report of United States Steel Corporation (the “Corporation”) on Form 10-K for the year ending December 31, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, John P. Surma, President and Chief Executive Officer of the Corporation, 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 and results of operations of the Corporation.

            /s/ John P. Surma

                 John P. Surma

                 President and Chief Executive Officer

February 25, 2005

A signed original of this written statement required by Section 906 has been provided to United States Steel Corporation and will be retained by United States Steel Corporation and furnished to the Securities and Exchange Commission or its staff upon request.