UPDATED 11.20PM: Wreckage, dozens of bodies and a plane-like shadow on the seabed have been found in the search of the missing AirAsia jet, prompting raw scenes of emotion from sobbing relatives of the 162 people aboard.

The Airbus A320-200 disappeared en route from Indonesia's second largest city Surabaya to Singapore during a storm early Sunday.

All indications now are that it crashed in the Java Sea southwest of the island of Borneo, with debris and dozens of bodies retrieved so far.

An air force plane saw a "shadow" on the seabed believed to be of the missing Flight QZ8501, National Search and Rescue Agency chief Bambang Soelistyo told a news conference in Jakarta.

Relatives of the 162 missing hugged each other and burst into tears in Surabaya as they watched footage of one body floating in the sea on a television feed of Soelistyo's press conference.

An Indonesian warship had recovered more than 40 bodies from the sea "and the number is growing", navy spokesman Manahan Simorangkir said shortly afterwards.

AirAsia's flamboyant chief executive, Tony Fernandes, expressed his grief over the first fatal incident to hit the region's biggest budget airline.

"My heart is filled with sadness for all the families involved in QZ 8501," Fernandes said on Twitter, adding that he was rushing to Surabaya.

Initial news of the debris dimmed the faint hopes of relatives of those missing.

"If that news is true, what can I do? I cannot bring him back to life," said Dwijanto, 60, whose son was on the plane along with five colleagues.

"My heart will be totally crushed if it's true. I will lose a son," he said.

Search chief Soelistyo said all efforts were now being concentrated on the location where the "shadow" and debris had been found, about 160 kilometres southwest of the town of Pangkalan Bun in Central Kalimantan on Borneo island.

The town has the nearest airstrip and is not far from the plane's last known position.

President Joko Widodo was expected in Pangkalan Bun shortly before heading to Surabaya to meet the relatives, officials said.

Indonesian officials had already been preparing relatives for the worst, with Soelistyo saying Monday it was likely the plane was at "the bottom of the sea", based on its estimated position.

The aircraft lost contact early on Sunday about 40 minutes after take-off, after the crew requested a change of flight plan due to stormy weather.

In his last communication, the pilot said he wanted to avoid a menacing storm system, before all contact was lost.

The crash comes at the end of a disastrous year for Malaysian aviation.

Flight MH370 disappeared while flying from Kuala Lumpur to Beijing in March with 239 passengers and crew, and in July another Malaysia Airlines flight - MH17 - was shot down over unrest-hit Ukraine, killing all 298 on board.