Leases for oil- and/or gas-mining purposes covering such unallotted lands shall be offered for sale to the highest responsible qualified bidder, at public auction or on sealed bids, after notice and advertisement, upon such terms and subject to such conditions as the Secretary of the Interior may prescribe. Such advertisement shall reserve to the Secretary of the Interior the right to reject all bids whenever in his judgment the interest of the Indians will be served by so doing, and if no satisfactory bid is received, or the accepted bidder fails to complete the lease, or the Secretary of the Interior shall determine that it is unwise in the interest of the Indians to accept the highest bid, said Secretary may readvertise such lease for sale, or with the consent of the tribal council or other governing tribal authorities, a lease may be made by private negotiations: Provided, That the foregoing provisions shall in no manner restrict the right of tribes organized and incorporated under sections 16 and 17 of the Act of June 18, 1934 (48 Stat. 984) [25 U.S.C. 5123, 5124], to lease lands for mining purposes as therein provided and in accordance with the provisions of any constitution and charter adopted by any Indian tribe pursuant to the Act of June 18, 1934 [25 U.S.C. 5101 et seq.].