"The damage is so huge it can hardly be evaluated. It can be compared to an ecological catastrophe," the Interfax news agency quoted Alexander Tkachyov, the governor of Russia's Black Sea region of Krasnodar, as telling regional officials.
"Thirty thousand birds have died, and it's just impossible to count the loss of fish."
Russian officials have described the spillage of more than 2,000 tonnes of fuel oil into the Kerch Strait from the Russian tanker Volganeft-139 as one of the country's "worst environmental disasters in years".
About 165 rescuers had saved 35 crew members and were hunting for other seamen missing in the area, Viktor Beltsov, a spokesman for the Russian emergencies ministry, said.
The dead "may have been crew members of [a] dry cargo ship Nakhichevan
that sank in the port of Kavkaz," a spokesman told the Interfax news agency.
Three of four freighters that also sunk during the same storm on Sunday were carrying sulphur and the fourth contained scrap metal, officials said.
The hull of another tanker had cracked but the ship remains afloat.
Another six other ships have also run aground.
Russian officials said shipping in the area had been warned in advance of heavy storms but it appeared some captains had chosen to ignore the advice and put to sea.
The tanker Volganeft-139 was on its way from the port of Azov in the southern Russian region of Rostov to Kerch in Ukraine's eastern Crimea when high waves broke its hull early on Sunday, Russian media reported.
The tanker, designed primarily for rivers and in service since 1978, was carrying 4,000 tonnes of fuel oil as it traversed the Kerch Strait, a waterway running between the Azov and Black Seas.
Environmentalists, who have been given public support by Viktor Yanukovich, the Ukrainian prime minister, said the incident raised questions about safety standards for shipping in the region.
At Novorossiisk, Russia's second-largest port for exports of oil and oil products, officials had ordered tankers not to dock because a new storm was on its way.
The worsening weather, forecast to last until Tuesday evening, was hampering rescue operations, said Anatoly Yanchuk, a rescue department chief at Russia's transport ministry."We will continue efforts to find those five missing, but the chances of finding them are now smaller," he said in the port of Kavkaz overlooking the strait.