<PAGE>   1
                                                                     EXHIBIT 4.4

                               FIRST AMENDMENT TO
                      EQUITY REGISTRATION RIGHTS AGREEMENT

                  FIRST AMENDMENT, dated as of June 22, 2001 (this "AMENDMENT"),
to the Equity Registration Rights Agreement, dated as of June 30, 2000 (as
heretofore amended, supplemented or otherwise modified, the "REGISTRATION RIGHTS
AGREEMENT"), among ANC RENTAL CORPORATION, a Delaware corporation (the
"COMPANY"), and LEHMAN COMMERCIAL PAPER INC., as administrative agent under the
Amended and Restated Senior Loan Agreement, dated as of June 30, 2000 (the
"ADMINISTRATIVE AGENT").

                              W I T N E S S E T H:

                  WHEREAS, the Company has requested that the Administrative
Agent amend certain provisions of the Registration Rights Agreement; and

                  WHEREAS, the Administrative Agent has agreed to amend the
Registration Rights Agreement, but only upon the terms and subject to the
conditions set forth below;

                  NOW, THEREFORE, in consideration of the premises and mutual
agreements contained herein, and for other valuable consideration, the receipt
of which is hereby acknowledged, the Company and the Administrative Agent hereby
agree as follows:

         1. DEFINITIONS. All terms defined in the Registration Rights Agreement
shall have such defined meanings when used herein unless otherwise defined
herein.

         2. AMENDMENT TO SECTION 3(B)(I) (FILING OF SHELF REGISTRATION). Section
3(b)(i) of the Registration Rights Agreement is hereby amended by (a) deleting
the words "360 days following the Spin-Off Date" and substituting in lieu
thereof the words "15 days following the receipt of a written request from the
Administrative Agent or Holders of a majority in aggregate principal amount of
the Registrable Securities" and (b) deleting the words "90 days after the
Initial Maturity Date" and substituting in lieu thereof the words "105 days
after the receipt of such written request".

         3. AMENDMENT TO SECTION 3(B)(II) (LIQUIDATED DAMAGES). Clause 3(b)(ii)
of the Registration Rights Agreement is hereby amended by deleting the words "90
days from the Initial Maturity Date" and substituting in lieu thereof the words
"105 days after the receipt of a written request under Section 3(b)(i)".

         4. LIMITED AMENDMENT. Except as expressly amended herein, the
Registration Rights Agreement shall continue to be, and shall remain, in full
force and effect. This Amendment shall not be deemed to be a waiver of, or
consent to, or a modification or amendment of, any other term or condition of
the Registration Rights Agreement or to prejudice any other right or rights
which the Administrative Agent may now have or may have in the future under or
in connection with the Registration Rights Agreement or any of the instruments
or agreements referred to therein, as the same may be amended from time to time.


<PAGE>   2


         5. COUNTERPARTS. This Amendment may be executed by one or more of the
parties hereto in any number of separate counterparts (which may include
counterparts delivered by facsimile transmission) and all of said counterparts
taken together shall be deemed to constitute one and the same instrument.

         6. GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED
AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.




                                       2
<PAGE>   3



                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be executed and delivered by their respective duly authorized
officers as of the date first above written.

                                  ANC RENTAL CORPORATION


                                  By:   /s/ HOWARD D. SCHWARTZ
                                        -------------------------------------
                                        Name:   Howard D. Schwartz
                                        Title:  Sr. Vice President & Secretary



                                  LEHMAN COMMERCIAL PAPER INC.,
                                  as Administrative Agent

                                  By:   /s/ MICHELE SWANSON
                                        -------------------------------------
                                        Name:   Michele Swanson
                                        Title:  Authorized Signatory



                                       3