Governor Keiichi Inamine on Tuesday said he also requested the downsizing or relocation of US air bases of Kadena and Futenma away from Okinawa's densely populated main island.
In addition, he sought the revision of the Status of Forces Agreement, which grants the US military jurisdiction over its troops in many legal matters.
"If the situation proceeds in a way that is unsatisfactory to the Okinawan people, this could shake the Japan-US security relationship," he said in a speech at the Centre for Strategic and International Studies, a Washington thinktank.
"If the situation proceeds in a way that is unsatisfactory to the Okinawan people, this could shake the Japan-US security relationship"
Inamine, who described himself as a "conservative who supports the Japan-US security alliance", said he had lodged a similar request in Tokyo before he flew to Washington for meetings with US officials this week.
The governor is an elected politician but has limited influence on Tokyo's policies.
Japanese media quoted Foreign Minister Nobutaka Machimura as saying it was "hard to imagine" reducing the number of US marines on Okinawa to zero.
Last October, Japanese leaders were reported to have asked for the removal of 2000 to 3000 troops from Okinawa.
Angered by accidents, violent crimes and environmental issues, many people in Okinawa have called for reducing what they say is their unfair burden of hosting the bulk of the US military's 47,000 troops in Japan.
Okinawa, a string of islands 1600km southwest of Tokyo, has less than 1% of Japan's total land mass but hosts more than half of the US military presence in the country.