QuickLinks -- Click here to rapidly navigate through this document

Exhibit 32a

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

        In connection with the Annual Report of International Bancshares Corporation (the "Company") on Form 10-K for the year ended December 31, 2005, as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Dennis E. Nixon, President and Principal Executive Officer of the Company, certify, pursuant to 18 U.S.C. 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 (15 U.S.C. 78m or 78o(d)), as applicable; and

(2)

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

By:	/s/  DENNIS E. NIXON Dennis E. Nixon President and Principal Executive Officer
Date:	March 15, 2006

        The foregoing certification is being furnished solely to accompany the Report pursuant to 18 U.S.C. 1350, and not being filed for purposes of Section 18 of the Securities Exchange Act, as amended, and is not to be incorporated by reference into any filing of the Company, whether on and before or after the date hereof, regardless of any general incorporation language in such filing.

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

QuickLinks

Exhibit 32a

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