FORM 6-K
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                        REPORT OF FOREIGN PRIVATE ISSUER

                     PURSUANT TO RULE 13A-16 OR 15D-16 UNDER
                       THE SECURITIES EXCHANGE ACT OF 1934



For June 4, 2004
Commission File Number:   0-30204
                          -------

                         INTERNET INITIATIVE JAPAN INC.
                 (Translation of registrant's name into English)
 JINBOCHO MITSUI BLDG. 1-105 KANDA JINBO-CHO, CHIYODA-KU, TOKYO 101-0051, JAPAN

                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F:

                      Form 20-F [ X ]          Form 40-F [ ]

     Indicate by check mark if the registrant is submitting the Form 6-K in
paper as per-mitted by Regulation S-T Rule 101(b)(1): ____

     Note: Regulation S-T Rule 101(b)(1) only permits the submission in paper of
a Form 6-K if submitted solely to provide an attached annual report to security
holders.

     Indicate by check mark if the registrant is submitting the Form 6-K in
paper as per-mitted by Regulation S-T Rule 101(b)(7): ____

     Note: Regulation S-T Rule 101(b)(7) only permits the submission in paper of
a Form 6-K if submitted to furnish a report or other document that the
registrant foreign private issuer must furnish and make public under the laws of
the jurisdiction in which the reg-istrant is incorporated, domiciled or legally
organized (the registrant's "home country"), or under the rules of the home
country exchange on which the registrant's securities are traded, as long as the
report or other document is not a press release, is not required to be and has
not been distributed to the registrant's security holders, and, if discussing a
mate-rial event, has already been the subject of a Form 6-K submission or other
Commission filing on EDGAR.

     Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                        Yes [   ]                No  [ X ]

     If "Yes" is marked, indicate below the file number assigned to the
registrant in connection with Rule 12g3-2(b): 82-_______________________

      THIS REPORT ON FORM 6-K SHALL BE DEEMED TO BE INCORPORATED BY REFERENCE IN
THE PROSPECTUS INCLUDED IN THE REGISTRATION STATMENT ON FORM F-3 (FILE NO.
333-12696) OF INTERNET INITIATIVE JAPAN INC. AND TO BE A PART THEREOF FROM THE
DATE ON WHICH THIS REPORT IS FURNISHED, TO THE EXTENT NOT SUPERSEDED BY
DOCUMENTS OR REPORTS SUBSEQUENTLY FILED OR FURNISHED.







                                  EXHIBIT INDEX


   Exhibit      Date         Description of Exhibit
------------  ---------      ----------------------
      1       6/4/2004       IIJ Announces the Acquisition of
                             Additional Shares of IIJ-MC







                                   SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                       Internet Initiative Japan Inc.




Date:  June 4, 2004                    By: /s/  Koichi Suzuki
                                       -------------------------------------
                                       Koichi Suzuki
                                       President, Chief Executive Officer and
                                       Representative Director