The biggest piece, measuring 18 meters (59 feet) long and 5.4 meters (18 feet) wide, appeared to be part of the jet's body, said Henry Bambang Soelistyo, chief of the National Search and Rescue Agency.
Though strong currents and big surf have prevented divers from entering waters to get a visual of the suspected fuselage, officials are hopeful they will find many of the passengers and crew inside, still strapped in their seats.
There were 162 people aboard the plane, but after a week of searching, only 30 bodies have been found floating in the choppy waters.
The Airbus A320 crashed Dec 28, 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 that 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, though bad weather appears to have been a factor, according to a 14-page report released by Indonesia's Meteorology, Climatology and Geophysics Agency.
"Flight 8501 appears to have been trapped in bad weather that would have been difficult to avoid," the report said.
While the plane's black boxes - the flight data and cockpit voice recorders - have yet to be located, the discovery of the wreckage, especially if it is largely intact, would greatly benefit the investigation.
The objects on the seafloor were discovered Friday and Saturday, and an Indonesian Geological Survey vessel was used to assess their dimensions, Soelistyo said.
In addition to what appeared to be a significant part of the plane's body, chunks of debris found in the target search area measured up to 12 meters (39 feet) long.
Other suspected plane parts were seen scattered on beaches during an aerial survey, Soelistyo said.
Indonesian authorities announced the grounding of AirAsia flights from Surabaya to Singapore, with the Transport Ministry saying the airline did not have a permit to fly on Sundays. However, Singapore's Civil Aviation Authority said Saturday that from its end, the airline had been approved to fly the route daily.