U.S. Navy Harrier fighter jets were forced to drop the bombs, two inert and two carrying explosives but not armed, after civilian boats were spotted near their original target.
The aircraft, which were not able to land safely carrying the bombs, were participating in Operation Talisman Saber, a joint U.S.-Australian military exercise involving nearly 30,000 personnel, mostly around northern Australia.
Vice Admiral Scott Swift, the commander of the U.S. 7th Fleet, said a decision on whether to leave the bombs or retrieve them was up to the Australian government.
"Once that determination has been made, we'll work closely with whoever is designated to remediate the problem. If that means removal of the weapons, I'd be happy to participate," Swift told media aboard an aircraft carrier, the U.S.S. George Washington, 200 km (125 miles) off the Australian coast.
The bombs were lying in 50 to 60 metres (160 ft to 200 ft) of water, posed little risk to the reef or shipping and could easily be picked up by Navy divers, a spokesman added.
Environmentalists have criticised holding such large-scale military exercises in sensitive areas such as the Great Barrier Reef, which is under threat from increased commercial shipping, climate change and an invasive starfish infestation, the United Nations says.
Swift and Australian Brigadier General David Coghlan said the site had been used for decades and the risks were manageable.
"We have a long history of good stewardship in that area and we have a solid environmental programme," Coghlan said. "We look at the risk every year, every day."
The Associated Press reported that the Great Barrier Reef Marine Park Authority, the government manager of the 345,400 square kilometer (133,360 square miles) protected marine zone, said in a statement that identifying options for the "rapid recovery" of the bombs so that they could pose no risk to the marine park was "a high priority."
But the authority also said the ordnances posed a "low risk to the marine environment."
"Based on where the ordnance have been dropped in a location that is in water around 50 meters (164 feet) deep, about 30 kilometers (19 miles) from the nearest reef and 50 kilometers (31 miles) from the shoreline, the immediate impact on the marine environment is thought to be negligible," the statement said.
(Reporting by ; Editing by Clarence Fernandez)