Nine bodies have so far been recovered from the Airbus A320-200, which crashed on Sunday en route to Singapore from the Indonesian city of Surabaya with 162 people on board.
The bodies were brought in numbered coffins to Surabaya where relatives have gathered for identification. AirAsia Indonesia's CEO Sunu Widyatmoko was seen weeping when authorities handed over the body of the first victim, Hayati Luthfiah Hamid, to family members at a Surabaya hospital.
Hamid, 49, was buried on Thursday before sundown in the suburb of Desa Sawotratap, a few kilometres (miles) from the city, at an Islamic ceremony attended by relatives and neighbours. Three members of her family were also on board the plane.
"Their house has been in a panic since Sunday," Umaroyah, a neighbour, said. "Everyone in the neighbourhood knows someone who was on that plane."
Searches on Thursday spanned an area of 13,500 square km (5,200 square miles) involving 19 ships, four helicopters and five planes, said Fransiskus Bambang Soelistyo, head of Indonesia's Seach and Rescue Agency.
A search and rescue pilot has spotted a large shadow in the sea, which rescuers believe may be the wreckage, but they have made clear the sighting is not yet confirmed.
"Until now, there hasn't been a confirmed finding or sonar image of the plane body under water," Soelistyo said.
Forty-seven divers are on standby to investigate.
"I am hoping that the latest information is correct and aircraft has been found," airline boss Tony Fernandes tweeted on Thursday. "Please all hope together. This is so important."
Toos Sanitiyoso, an air safety investigator with the National Committee for Transportation Safety, said it could take a week to find the black box. Committee head Tatang Kurniadi said the focus of the search, once the waters had calmed as expected in five days, was around the shadow.
"We are backtracking from where the wreckage was found to where the plane had its last reading and that is the focus of our search," Kurniadi said. "The depth around here is 50 metres. No specialist equipment (is required). Divers can go get it."
Investigators are working on a theory that the plane stalled as it climbed steeply to avoid a storm about 40 minutes into the flight.
"What is most difficult is finding the location where the plane fell - checking whether the aircraft is really there," frogman commander Lieutenant Edi Tirkayasa told Reuters. "With weather like this, who knows? We are still hopeful and optimistic that they'll find it. They must." So far, as well as the bodies, debris including a suitcase, an emergency slide and a life jacket have been recovered from waters near the suspected crash site. No survivors have been found. All but seven of those on board were Indonesians.
Authorities have been collecting DNA from relatives to help identify the bodies.
"We are asking universities to work with us - from the whole country," said Anton Castilani, executive director at Indonesia's disaster victims identification committee.
Relatives, many of whom collapsed in grief when they saw the first television pictures confirming their fears on Tuesday, held prayers at a crisis centre at Surabaya airport.
"UNBELIEVABLY" STEEP CLIMB
The plane was travelling at 32,000 feet (9,753 metres) and had asked to fly at 38,000 feet to avoid bad weather. When air traffic controllers granted permission for a rise to 34,000 feet a few minutes later, they received no response.
A source close to the investigation said radar data appeared to show that the aircraft made an "unbelievably" steep climb before it crashed.
"It appears to be beyond the performance envelope of the aircraft," he said, noting that more information was needed to come to a firm conclusion.
Online discussion among pilots has centred on unconfirmed secondary radar data from Malaysia that suggested the aircraft was climbing at a speed of 353 knots, about 100 knots too slow, and that it might have stalled.
The Indonesian captain, a former air force fighter pilot, had 6,100 flying hours under his belt and the plane last underwent maintenance in mid-November, according to AirAsia Indonesia, which is 49-percent owned by Malaysia-based budget carrier AirAsia.
Three airline disasters involving Malaysian-affiliated carriers in less than a year have dented confidence in the country's aviation industry.
Malaysia Airlines Flight MH370 disappeared in March en route to Beijing from Kuala Lumpur and has not been found. On July 17, the same airline's Flight MH17 was shot down over Ukraine.
The AirAsia group, including affiliates in Thailand, the Philippines and India, had not suffered a crash since its Malaysian budget operations began in 2002.
Separately, an AirAsia Indonesia pilot was taken off flying duties on the route from Jakarta to the holiday island of Bali on Thursday after a urine test indicated traces of morphine. The airline said he had been taking medication following an illness.