Three marines went missing in the crash.
The Marine Corps did not say what caused the crash, but indicated it is under investigation.
"He would sacrifice himself in a minute to make sure that his fellow service members were safe", Cross said.
In 2015, a U.S. Osprey crashed during a training exercise in Hawaii, killing two Marines.
The MV-22 Osprey crashed in Shoalwater Bay with 26 people on board after taking off from the U.S. Navy's USS Bonhomme Richard assault ship on Saturday, off the Queensland coast.
The Osprey, which was assigned to Marine Medium Tiltrotor Squadron 265 on Okinawa, was in Australia as part of the Australian-U.S. military exercise Talisman Sabre, which concluded at the end of July. The deck of the USS Green Bay was damaged in the incident.
The hybrid aircraft, which is created to fly like an airplane but take off and land like a helicopter, entered service with the Marine Corps in 2007.
Davis, who declined to confirm the Marines were considering the stand down, said U.S. Forces-Japan officials were in discussions about the incident with the Japanese government.
The Marines had just wrapped up a major exercise with Australian forces and on Saturday were conducting training of their own when the accident happened.
Ospreys were grounded in Japan last December after pilots ditched one in shallow water just off Camp Schwab in northern Okinawa. The incident is under investigation, and it is unclear why the Osprey crashed, though landing and taking off from ships at sea is often hard and inherently unsafe.
Japan plans to discuss with the USA whether it would be appropriate for Ospreys to take part in joint training between the Japanese Ground Self-Defense Force and the U.S. Marines in Japan's island of Hokkaido, planned to be held from Thursday, Defense Minister Itsunori Onodera told reporters Sunday as reported by Kyodo news agency.