Flight QZ8501 was flying from Surabaya, Indonesia to Singapore on 28 December when it disappeared from radar.
Search teams have recovered 37 bodies but the remains of most victims are thought to still be in the plane.
Bad weather has hampered attempts to reach large objects thought to be the body of the plane.
Officials told the BBC’s Indonesian service on Monday that sonar equipment had been deployed underwater, but that the weather meant no divers were yet back in the water.
The head of Indonesia’s search and rescue agency, Bambang Soelistoyo, said in a news briefing that three more bodies were recovered on Monday.
He added that weather conditions had improved since last week, but that the currents underwater were still strong.
Dozens of ships and aircraft are involved in the operation.
The families of the passengers have been offered a chance to fly to the location believed to be the crash site and lay flower wreaths, the commander of the Armed Forces, Gen Moeldoko, said in Surabaya.
They would fly to Pangkalan Bun, the nearest town, then be taken by a naval ship to the location in the Java Sea. He said he believed this might help “reduce their sadness and the feeling of loss”.
Gen Moeldoko also assured the families that all the victims would be identified regardless of their condition when found.
He said 260 national and international doctors were working to identify the remains recovered using finger prints, dental records and bone DNA.
Four large objects thought to be debris from the plane were spotted on Saturday, with the largest measuring 18m (59ft) by 5.4m, at a depth of 30m.
A fifth object, measuring 9.8m by 1.1m, was located on the seabed on Sunday but teams could not reach them to confirm they came from the AirAsia flight.
Divers from Indonesia and Russia have been deployed to the search area, which has been enlarged to allow for tides sweeping bodies and debris further afield.
They attempted to survey more of the seabed on Sunday but “visibility at the sea bottom was zero”, search and rescue chief Bambang Soelistyo said.
Remotely operated cameras were being used to try to photograph the objects, but waves up to 5m (16ft) high and strong currents made their use difficult.
National Search and Rescue deputy chief Tatang Zainudin said: “We are racing with time and weather in running this mission.”
Officials have said the plane was travelling at 32,000ft when the pilot’s last communication was a request to climb to 38,000ft to avoid bad weather.
On Saturday, Indonesian weather agency BMKG said initial analysis suggested icy conditions in the air had caused the engine to stall.
It has emerged that AirAsia did not have official permission from Indonesia to fly the Surabaya-Singapore route on the day of the crash, but was licensed on four other days of the week.
However, a statement from the civil aviation authority in Singapore said that AirAsia did have permission from them to operate the flight daily.
The Indonesian authorities have now suspended the company’s flights on this route pending an investigation.
AirAsia – which previously had an excellent safety record with no fatal accidents involving its aircraft – said it would “fully co-operate”.
At a press conference on Monday, Djoko Murjatmojo from the transportation ministry said the air traffic control officer at Juanda Airport in Surabaya on duty at the time of the accident had been temporarily suspended.
He also said that AirAsia had violated the flight permission for the Singapore-Surabaya route for at least two months before the accident.
There were 137 adult passengers, 17 children and one infant, along with two pilots and five crew, on the plane – the majority Indonesian.