Indonesia has found the cockpit voice recorder from a Lion Air plane more than two months after the Boeing Co 737 MAX jet crashed into the sea near Jakarta, killing all 189 people on board, search officials have said.

Naval Lieutenant Colonel Agung Nugroho told Reuters a weak signal from the recorder had been detected for several days and that it had been found buried in about 8 metres of mud in waters about 30 metres deep.

"We don't know what damage there is, it has obvious scratches on it," Mr Nugroho said.

Contact with flight JT610 was lost 13 minutes after it took off on 29 October from the capital, Jakarta, heading north to the tin-mining town of Pangkal Pinang.

The crash was the world's first of a Boeing 737 MAX jet and the deadliest of 2018.

The cockpit voice recorder is one of the two so-called black boxes crucial for the investigation of a plane crash.

The other black box, the flight data recorder, was recovered three days after the crash.

Investigators brought in a navy ship last week for a fresh search after a ten-day effort funded by Lion Air failed to find the recorder.

Separately, Colonel Johan Wahyudi told Metro TV the recorder had been retrieved and taken aboard the ship.

Boeing did not respond immediately to a request for comment.

A preliminary report by Indonesia's transport safety commission, or KNKT, focused on airline maintenance and training, as well as the response of a Boeing anti-stall system and a recently replaced sensor, but did not give a cause for the crash.