The aircraft, an MV-22 Osprey, crashed at Shoalwater Bay near Rockhampton on Saturday afternoon. Boats and aircraft on the ship immediately launched a search and rescue effort.
The Osprey, built by Boeing Co and Textron Inc's Bell Helicopter unit, is created to take off like a helicopter and rotate its propellers to fly like a plane.
MV-22s have been involved in several serious crashes, some of them fatal, in the 10 years they have been used by the U.S. military.
The Bonhomme Richard Expeditionary Strike Group was in Australia to participate in joint training manoeuvres involving more than 33,000 United States and Australian military personnel, which ended two weeks ago.
The recent joint military exercise took place largely in Shoalwater Bay and involved more than 30,000 U.S. and Australian personnel, according to Australian Defense Department.
Minister for Defence Marise Payne confirmed in a statement late on Saturday night that no Australian Defence Force personnel were on board the aircraft.
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U.S. military officials, who described the crash as a "mishap", have turned their efforts to salvage and recovery, which they warn could take several months.
Onodera, who assumed his post in a cabinet reshuffle on Thursday, said Japan also urged Washington to disclose information about the accident, investigate what caused it and take measures to prevent such an accident from happening again.
Three crew members are still missing after the United States Marine Corps (USMC) MV-22 Osprey "entered the water" on Saturday afternoon.
A squadron of Ospreys is based at the Marines' Futenma base on the southern Japanese island of Okinawa.
Twenty-three of the crew members were rescued within an hour. In January, three USA soldiers were injured in a "hard landing" of an Osprey in Yemen. In its deadliest incident, 19 Marines were killed in April 2000 while trying to land during a training exercise in Arizona.
The Marines began training in the aircraft 15 years ago.
The White House said that President Trump was briefed on the matter by his chief of staff, John Kelly.