The Secretary of the Interior shall issue quitclaim deeds to the public-land States for all lands patented to such States under section 641 of this title. He shall also issue a patent for all unpatented public lands within each State now segregated under that section for which the State issued final certificates or other evidence of right prior to June 1, 1953, or as to which equitable claims to the lands accrued prior to that date (by reason of cultivation or improvement of the lands for agricultural development purposes) for conveyance to the holders of such rights or claims, or to their heirs, successors, or assigns.