Russian rescuers working round the clock have found the main black box from the Syria-bound military plane that crashed into the Black Sea with 92 people on board, authorities said.

The defence ministry said the box, which could provide vital clues as to why the Tu-154 jet crashed, was discovered early Tuesday only 1,600 metres from the shore and 17 metres under the surface and was in "satisfactory condition".

Investigators were also looking at a witness video of the abortive flight and the plane's plunge into the sea.

The Tu-154 jet, whose passengers included more than 60 members of the internationally renowned Red Army Choir, was heading to Russia's military airbase in Syria on Sunday when it went down off the coast of Sochi shortly after take-off from a refuelling stop at the airport.

Investigators said they have sorted and documented thousands of passengers' personal items and identification documents, questioned locals and are checking the fuel equipment at the airport.

One witness "filmed the takeoff, flight and fall of the plane into the sea," the Investigative Committee said in a statement.

The discovery of the black box comes as searchers scramble to recover bodies and remaining debris from the aircraft in an operation involving divers, deepwater machines, helicopters and drones.