JAKARTA (REUTERS/AFP) - Scores of divers plunged into the Java Sea on Thursday to search the wreckage of an AirAsia jet for the black box recorders that could reveal why the plane crashed, Indonesia's search and rescue agency said, as a Malaysian search vessel found a female body.

Divers from the Indonesian Marines' elite diving unit battled strong currents in an effort to reach the submerged tail of the plane, but the currents stymied efforts on Thursday morning to penetrate into the tail, search and rescue agency chief Bambang Soelistyo told reporters in Jakarta.

"Divers have reached the tail part but... the visibility was below one metre so they only managed to retrieve various debris," Mr Soelistyo said.

"Now we are waiting for the speed of the current to ease. If it gets calmer later, they will go back to do another dive to determine whether the black boxes remained in the tail or were detached."

He said retrieval experts were also ready with a crane to lift the tail out of the water.

However, he said a decision on extracting the tail would not be made until a more through inspection of it was carried out, with the continuing storm weather another factor.

Mr Soelistyo said the other top priority was the search for bodies, with just 40 found so far floating at sea.

Many of the others are believed to be inside the wreckage of the plane's main cabin, which has not been found.

In the meantime, Malaysia's search vessel KD Perak recovered a female body on Thursday, Malaysia's Chief of Navy Abdul Aziz Jaafar said in a tweet.

The tail of the plane - flight QZ8501 - was found on Wednesday, upturned on the sea bed about 30 km from the plane's last known location at a depth of around 28-32 metres.

"After we found the tail, our plan is to do everything step by step," Fransiskus Bambang Soelistyo, head of the search and rescue agency, told a news conference in Jakarta.

"First we will (check whether) the black box is still at its place, in the tail, or if it has detached."

A total of 84 divers were in ships in the vicinity and teams began searching the jet's tail on Thursday morning, with visibility poor and strong currents still impeding efforts, Soelistyo added.

Should diving teams confirm the location of the recorders, the tail will probably be plucked out of the sea using a crane capable of lifting 70 tonnes.

Ships with acoustic "pinger locators" designed to pick up signals from the black boxes were at the location but were no longer being used, in a possible sign of confidence among Indonesian officials that the recorders will be found soon.

Two Japanese ships that were part of the international effort to find the plane would now leave the mission on Friday, Soelistyo added.

"Now that the tail is confirmed, we are confident," Mardjono Siswosuwarno, the main investigator of the National Transportation Safety Committee, told Reuters late on Wednesday.

"In my opinion, the pinger locators are no longer necessary to finding the black box."

Flight QZ8501 vanished from radar screens over the northern Java Sea on Dec 28, less than half-way into a two-hour flight from Indonesia's second-biggest city of Surabaya to Singapore. There were no survivors among the 162 people on board.

The cause of the crash remains a mystery, with hopes centring on the so-called black boxes - the flight data recorder and the cockpit voice recorder - providing vital clues.

The plane which crashed was an Airbus A320-200, which carries the recorders near the tail section.

Forty bodies and debris from the plane have been plucked from the surface of the waters off Borneo, but strong winds and high waves have been hampering divers' efforts to reach larger pieces of suspected wreckage detected by sonar on the sea floor.

In Pangkalan Bun, the southern Borneo town closest to the crash site, Indonesian armed forces chief Moeldoko said he would personally lead any mission to lift the jet's tail.

Weather agency officials warned on Thursday that although weather conditions at search areas had improved over the last two days, it was likely to worsen from Friday onwards.

Indonesia AirAsia, 49 per cent owned by Malaysia-based AirAsia budget group, has come under pressure from the authorities in Jakarta since the crash.

The transport ministry has suspended the carrier's Surabaya-Singapore licence, saying it only had permission to fly the route on Mondays, Tuesdays, Thursdays and Saturdays.

Flight QZ8501 took off on a Sunday, though the ministry said this had no bearing on the accident.

AirAsia has said it is cooperating fully with the ministry's investigations. That investigation would be completed by Friday evening, the transport ministry said.