TOKYO — A long-simmering dispute between the United States and Japan over the fate of a Marine base on Okinawa seemed to have been resolved on Friday when the governor of Okinawa gave his approval to move the base to a remote area.

The agreement would bolster efforts by the Pentagon to rebalance American military forces across the Asia-Pacific region and by the Japanese prime minister, Shinzo Abe, to raise his country’s strategic posture and check the growing military influence of China.

An official document approving a landfill on which much of the base would be built was stamped by the governor of Okinawa, Hirokazu Nakaima, and sent to the local branch of the Ministry of Defense, Kanako Shimada, a prefectural official, said on Friday.

Mr. Nakaima’s approval was a breakthrough after what had been longstanding opposition on Okinawa to the plan to move the Marine Corps’ Air Station Futenma, on the prefecture’s main island to the north of the island.