Two Russian oil tankers with 29 crew members on board have sunk in the Black Sea amid bad weather and are now leaking oil, Russian authorities have said.

Video posted on Telegram by Russia's Southern Transport Prosecutor's Office, which the BBC has been unable to verify, appears to show one of the tankers broken in half and sinking amid a heavy storm, with streaks of oil visible in the water.

At least one crew member is believed to have died - and Russian authorities are investigating for criminal negligence, according to TASS news agency.

The incident took place in the Kerch Strait, which separates Russia from occupied Crimea.

A rescue and clean-up operation is under way involving tugboats, helicopters and more than 50 personnel, TASS news agency reported.

"Today, as a result of a storm in the Black Sea, two tankers, Volgoneft-212 and Volgoneft-239, sank," Russia's federal sea and inland water transport agency, Rosmorrechflot, wrote in a statement.

"There were crews of 15 and 14 people on board the ships. The accident resulted in a spill of oil products," it continued.

Both tankers have a loading capacity of about 4,200 tonnes of oil, Reuters news agency reported.

The full extent of the oil spill remains unclear.