One tanker sank and another ran aground on December 15 in the Kerch Strait between Russia and the annexed Crimean peninsula.
Thousands of volunteers have been mobilised for clean-up operations that have been criticised as insufficent by some Russian scientists.
The tankers were carrying 9,200 tonnes of fuel oil, around 40 percent of which may have spilled into the sea, according to authorities.
"The situation is truly critical," said Kremlin spokesman Dmitry Peskov, quoted by Russian press agencies.
"It is unfortunately impossible to calculate for the moment the extent of the environmental damage but specialists are working regularly on it," he said.
The Moscow-installed governor of Crimea, Sergei Aksionov, said on Telegram he had declared a state of emergency "because of the oil products spill in the Kerch Strait".
Russia's transport ministry insisted on Saturday that "all polluted aquatic areas that have been identified have been cleaned" and "no recurring pollution has been detected".
But Emergency Situations Minister Alexander Kurenkov was more cautious, saying: "The threat of a new fuel oil leak in the Black Sea from the tankers and spills on the coast persists".
President Vladimir Putin earlier this month called the oil spill an "ecological disaster".
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