Exhibit 32

CERTIFICATION OF CHIEF EXECUTIVE OFFICER AND

CHIEF FINANCIAL OFFICER PURSUANT TO RULE 13a-14(b) UNDER

THE SECURITIES EXCHANGE ACT OF 1934 AND SECTION 1350 OF

CHAPTER 63 OF TITLE 18 OF THE UNITED STATES CODE

Each of the undersigned, Francis P. Grillo and David W. Carlson, certifies pursuant to Rule 13a-14(b) under the Securities Exchange Act of 1934 and Section 1350 of Chapter 63 of Title 18 of the United States Code, that (1) this quarterly report on Form 10-Q for the quarter ended March 31, 2015, of MRI Interventions, Inc. (the “Company”) fully complies with the requirements of Section 13(a) of the Securities Exchange Act of 1934, and (2) the information contained in this report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: May 7, 2015