Teams equipped with a remote-operated vehicle were battling high waves and strong currents as they tried to capture images of the find for confirmation, said Henry Bambang Soelistyo, chief of the National Search and Rescue Agency.
The objects were detected early Friday by an Indonesian navy ship, and by midnight, searchers had zoomed in with a Geological Survey ship to take dimensions.
One was measured at 9.4 metres by 4.8 metres (31 feet by 15 feet) and a half-meter (20 inches) high, Soelistyo told a news conference. The second, found nearby, was 7.2 metres (24 feet) by a half meter (20 inches).
"I'm confident this is part of the AirAsia plane," Soelistyo told reporters.
The Airbus A320 carrying 162 passengers and crew crashed last Sunday, halfway into a two-hour flight from Surabaya, Indonesia's second-largest city, to Singapore. Minutes before losing contact, the pilot told air traffic control he was approaching threatening clouds, but was denied permission to climb to a higher altitude because of heavy air traffic.
It remains unclear what caused the plane to plunge into the Java Sea.
Indonesian authorities on Friday grounded AirAsia flights from Surabaya to Singapore, with the Transport Ministry saying the airline did not have a permit to fly on Sundays, the day of the crash. AirAsia, which began operations in 2001, quickly becoming one of the region's most popular low-cost carriers, said it was reviewing the suspension.
Rough weather has hampered recovery efforts, with only 30 corpses recovered so far, many of them by a U.S. Navy ship.
Vessels involved in the hunt included at least eight sophisticated navy ships from Singapore, Russia, Malaysia and the U.S. equipped with sonars for scouring the seabed to pinpoint wreckage and the all-important black boxes.
"Many of passengers believed to be still trapped inside the plane's fuselage and could be discovered soon," Supriyadi said, "God willing, we would complete this operation next week."
Associated Press writers Niniek Karmini, Ali Kotarumalos and Robin McDowell in Jakarta and Eileen Ng in Surabaya, Indonesia, contributed to this report.