Australia's Sunday Telegraph newspaper said two people were missing and feared dead, with unconfirmed reports that the rest of the 25 personnel on board had been rescued.
Both ships and aircraft have been scrambled to aid the search operation.
It was in Australia for the recent Talisman Sabre military exercise - a biennial event involving Australia and the United States, which involved more than 30,000 troops and 200 aircraft.
The US Marine Corps said in a statement small boats and aircraft were involved in the search. More than 33,000 US and Australian military personnel, including the Bonhomme Richard Expeditionary Strike Force, participated in the drills, which wrapped up on July 25, the USA military said.
The Marine base Camp Butler in Japan said that 23 of 26 personnel aboard the aircraft have been rescued after Saturday's crash. Its five crew members were rescued safely.
The aircraft, resembling a cross between a helicopter and airplane, has capabilities including taking off vertically and travelling much faster than a helicopter.
In 2015, a U.S. Osprey crashed during a training exercise in Hawaii, killing two Marines.
The United States and Australia have a long history of military partnership, including cooperation in the coalition during the Afghanistan and Iraq wars.
'I have briefed Prime Minister Turnbull and spoken with Secretary Mattis this evening to offer Australia's support in anyway that can be of assistance'. According to MSN, the U.S Marine Corps said that the incident was under investigation but would give no further comment. Ospreys are a cross between a helicopter and plane and have been involved in a number of recent crashes. Military sources told the newspaper the accident occurred as the aircraft attempted to land on the USS Ronald Reagan.