Indonesia's President Joko Widodo (R) walks beside AirAsia's CEO Tony Fernandes after meeting with family members of passengers onboard AirAsia flight QZ8501 in Juanda International Airport, Surabaya December 30, 2014. [Photo/Agencies]

AirAsia Chief Executive Tony Fernandes, who has described the crash as his "worst nightmare", was rushing to Surabaya where relatives of the missing are gathered at a crisis centre in Indonesia's second-largest city.

Widodo said AirAsia would pay an immediate advance of money to the families, many of whom collapsed in grief when they saw the television pictures of debris.

The navy initially said 40 bodies had been recovered, although other media later quoted the head of the search and rescue agency, Fransiskus Bambang Soelistyo, as saying only three bodies had been retrieved.

Dozens of Indonesian navy divers are expected to begin the underwater search at first light on Wednesday, a source close to the investigation said.

The United States said its missile-guided destroyer USS Sampson and combat ship USS Fort Worth were awaiting instructions from the Indonesian search command on the recovery operation. Singapore said it was sending two underwater beacon detectors to try to pick up pings from the black boxes, which contain cockpit voice and flight data recorders.

About 30 ships and 21 aircraft from Indonesia, Australia, Malaysia, Singapore, South Korea and the United States have been involved in the search.