Salvage teams have recovered a British stealth fighter that fell into the Mediterranean as it was taking off from the UK's flagship aircraft carrier, NATO and British officials said on Wednesday.

"Operations to recover the UK F-35 jet in the Mediterranean Sea have successfully concluded," Britain's defence ministry said in a tweeted statement.

NATO Air Command tweeted that "NATO allies Italy and the United States of America supported during the recovery operation".

The sophisticated, US-made F-35B plunged into the sea on November 17 as it was taking off from HMS Queen Elizabeth, Britain's top aircraft carrier, which was returning from a mission in the Indo-Pacific. 

A video taken on board and published by British media showed the jet moving slowly up the ramp at the end of the ship's runway and falling into the water. The pilot safely ejected.

UK Defence Journal, an online outlet focused on the British military, reported on Tuesday that a sailor suspected of leaking the footage was arrested and flown back to Britain.

A report in Britain's The Sun newspaper said British defence officials believe a plastic engine cover had been left over one of the jet intakes of the plane, causing it to crash. 

British and NATO officials on board HMS Queen Elizabeth told AFP on November 22 they were confident of salvaging the wreck of the plane before Russia might get to it with its recovery vessels.

The officials did not give any details of the recovery operation, citing the need for secrecy.

Britain has so far taken delivery of 21 of the US-made F-35Bs, mostly for its two modern aircraft carriers, HMS Queen Elizabeth and HMS Prince of Wales. Each jet costs more than 100 million euros ($110 million).

The F-35Bs are designed for short take-off and vertical landing, and are a variant from other F-35s. They are fifth generation war planes able to be equipped for a range of different missions.