The alleged attack against a 19-year-old woman spurred Japan's prime minister to call Friday for stricter discipline among U.S. forces in Japan.
A district court in Okinawa granted police permission on Monday to arrest the Marine, the next step to bringing the suspect to trial, Kyodo News and public broadcaster NHK said.
Police spokesman Shinpachi Higashizato and U.S. Forces' Japan spokeswoman Master Sgt. Leah Gonzalez could not immediately confirm the report. A spokesman for the district court would also not confirm whether the warrant was issued.
The suspect is a 21-year-old Marine lance corporal based in Okinawa, home to more than half of the 47,000 U.S. troops stationed in Japan.
The attack allegedly occurred early May 25 in the town of Kin, according to a statement released last week by the Marines at Camp Butler.
Police say the suspect admitted punching the woman in an alley but denied raping her, saying sex was consensual, Kyodo reported. The woman reportedly suffered a broken nose. They had earlier met at a restaurant, Kyodo said.
On Friday, Prime Minister Junichiro Koizumi urged the U.S. military "to enforce strict discipline so this kind of incident does not take place."
Japanese media reported last week that police on Okinawa were questioning the suspect on a voluntary basis.
Okinawa is located about 1,000 miles southwest of Tokyo.
The handling of military suspects is an extremely sensitive issue in Okinawa. In 1995, the rape of a local schoolgirl by three U.S. servicemen triggered outrage on the island.