AirAsia has confirmed that the debris found in the sea is from its missing Airbus A320 aircraft.

As reports came through of bodies being recovered from the Java Sea, AirAsia Chief Executive Tony Fernandes said he was "absolutely devastated".

Indonesian rescuers searching for the plane have pulled dozens of bodies and wreckage from the sea off the coast of Borneo.

Relatives of those on board broke down in tears on hearing the news.

Flight QZ8501, an Airbus A320-200, lost contact with air traffic control early on Sunday during bad weather on a flight from the Indonesian city of Surabaya to Singapore.

The plane, which was carrying 162 people, has yet to be found and there was no word on the possibility of any survivors.

Pictures of floating bodies were broadcast on television and relatives of the missing gathered at a crisis centre in Surabaya wept with heads in their hands.

Several people collapsed in grief and were helped away, a Reuters reporter said.

"You have to be strong," the mayor of Surabaya, Tri Rismaharini, said as she comforted relatives.

"They are not ours, they belong to God."

A navy spokesman said a plane door, oxygen tanks and one body had been recovered and taken away by helicopter for tests.

AirAsia chief Tony Fernandes, who has been in Indonesia since the plane went missing, said he was rushing back to Surabaya.

"Whatever we can do at AirAsia we will be doing," he said on Twitter.

About 30 ships and 21 aircraft from Indonesia, Australia, Malaysia, Singapore, South Korea and the United States had been involved in the search of up to 10,000 square nautical miles.

The plane, which did not issue a distress signal, disappeared after its pilot failed to get permission to fly higher to avoid bad weather because of heavy air traffic, officials said.

Flight QZ8501 was travelling at 32,000ft and had asked to fly at 38,000ft, officials said earlier.

Pilots and aviation experts said thunderstorms, and requests to gain altitude to avoid them, were not unusual in that area.

The Indonesian pilot was experienced and the plane last underwent maintenance in mid-November, the airline said.

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 plane, whose engines were made by CFM International, co-owned by General Electric and Safran of France, lacked real-time engine diagnostics or monitoring, a GE spokesman said.

Such systems are mainly used on long-haul flights and can provide clues to airlines and investigators when things go wrong.

Three airline disasters involving Malaysian-affiliated carriers in less than a year have dented confidence in the country's aviation industry and spooked travellers across the region.

Malaysian Airlines Flight MH370 went missing on 8 March on a trip from Kuala Lumpur to Beijing with 239 passengers and crew on board and has not been found.

On 17 July, the same airline's flight MH17 was shot down over Ukraine, killing all 298 people on board.

On board flight QZ8501 were 155 Indonesians, three South Koreans, and one person each from Singapore, Malaysia and Britain. The co-pilot was French.