Exhibit 32.1

Certification Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

Pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, I, William G. Rice, the President and Chief Executive Officer of Aptose Biosciences Inc. (the “Company”), hereby certify that, to my knowledge:

1.
The Quarterly Report on Form 10-Q for the quarter ended March 31, 2024 (the “Report”) of the Company fully complies with the requirements of Section 13(a) or Section 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 Company.

Date: May 14, 2024

/s/ William G. Rice

Name: William G. Rice, Ph.D.

Title: President and Chief Executive Officer