Spilled oil has washed up along "tens of kilometres" of the Russian Black Sea coast after two tankers were badly damaged in a storm at the weekend, a regional official said on Tuesday, and state media said a third vessel was now in trouble.

TASS news agency said the third ship, also a tanker, had issued a distress signal off the port of Kavkaz, but its hull was still intact, there was no oil spillage and the crew was safe.

The first ship, the Volgoneft 212, split in half on Sunday in the Kerch Strait, between the Black Sea and the Sea of Azov. The second, the Volgoneft 239, ran aground 80 metres (87 yards) from the shore near the port of Taman in the strait.

The ships, both more than 50 years old, were carrying some 9,200 metric tons (62,000 barrels) of oil products in total, TASS reported, raising fears it could become one of the largest environmental disasters to hit the region in years. Another agency, RIA, said the third vessel was from the same ageing group of ships.

Veniamin Kondratyev, governor of the southern Krasnodar region, said fuel oil had been found along the coast between the towns of Temryuk and Anapa.

"This morning, while monitoring the shoreline, stains of fuel oil were discovered. Oil products washed ashore for several tens of kilometres," he said.

Authorities said a local state of emergency had been declared at four settlements in Temryuk district and one village in Anapa district because of spilled oil on the shoreline.

A video posted by Zvezda TV showed a black, oil-like substance along the coast at Anapa, and tarry stains along a beach strewn with tree branches.

TASS news agency, citing a scientist, said the nearby Kerch Strait, which separates Russia's Krasnodar region from the Crimean peninsula that Moscow annexed from Crimea in 2014, is an important area for migrating dolphins and other sea mammals.

"You can say they hit a key place," Dmitry Glazov of the Institute of Ecology and Evolution was quoted as saying.

A video broadcast by state TV channel Vesti showed several birds covered with oil flapping their wings and struggling to fly.

Russia's Natural Resources and Ecology Ministry said on Monday that fuel oil had leaked into the sea, but the scale of the spillage was still not clear.

Natural Resources and Ecology Minister Alexander Kozlov said some of the fuel oil could have sunk to the seabed due to cold weather.

The shipping industry has raised concern in recent months over the risks and potential for collisions posed by hundreds of "shadow" tankers in open sea lanes, with little incentive for these vessels to follow cleaner shipping standards.

The Kerch Strait is a key route for exports of Russian grain and fuel products.

One member of the Volgoneft 212's crew was killed in Sunday's accident, while all 14 people on the Volgoneft 239 were rescued.