Two Russian oil tankers with 29 crew members on board have been heavily damaged in the Black Sea, triggering an oil spill, authorities in Russia have said.

Footage released by Russia's Southern Transport Prosecutor's Office showed 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 was reportedly killed and the second ship was said to be drifting after sustaining damage.

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

President Vladimir Putin has ordered a working group to be set up to deal with the incident, headed by Deputy Prime Minister Vitaly Savelyev, local media reported.

Authorities are investigating for criminal negligence, according to TASS news agency.

A rescue and clean-up operation is said to be under way involving tugboats, helicopters and more than 50 personnel.

"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 and the exact fate of both ships remains unclear.

In 2007, another Volgoneft oil tanker - Volgoneft-139 - split in half during a storm while anchored off the Kerch Strait, spilling more than 1,000 tonnes of oil.