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                                                                    EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
                       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 Quarterly Report of First Real Estate Investment
Trust of New Jersey (the "Company") on Form 10-Q for the quarter ended January
31, 2004 (the "Report"), I, Robert S. Hekemian, Chairman of the Board and Chief
Executive Officer of the Company, do hereby certify, pursuant to 18 U.S.C.ss.
1350, as adopted pursuant to ss. 906 of the Sarbanes-Oxley Act of 2002, that to
my knowledge:

(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. ss. 78m(a) or 78o(d),
      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: March __, 2004                    /s/ Robert S. Hekemian
                                        -----------------------------
                                        Robert S. Hekemian
                                        Chairman of the Board and Chief
                                        Executive Officer