Exhibit 32.1

Certification Pursuant to 18 U.S.C. Sec. 1350
(Section 906 of the Sarbanes — Oxley Act of 2002)

In connection with the filing by HRPT Properties Trust (the “Company”) of the Quarterly Report on Form 10-Q for the period ending March 31, 2006 (the “Report”), each of the undersigned hereby certifies, to the best of his knowledge:

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 Company.

/s/ Barry M. Portnoy	/s/ John A. Mannix
Barry M. Portnoy	John A. Mannix
Managing Trustee	President and Chief
	Operating Officer
/s/ Gerard M. Martin	/s/ John C. Popeo
Gerard M. Martin	John C. Popeo
Managing Trustee	Treasurer and Chief
	Financial Officer