According to preliminary information, the fire broke out on Monday during a transfer of liquefied natural gas from one vessel to another.
Twelve people have been saved, Russia's Federal Agency for Sea and River Transport (Rosmorrechflot) told the Moscow-based Interfax news agency.
The BBC reported that one of the vessels, the Kandy, carried 17 crew members while the Maestro with 14 crew members. "The search and rescue operation continues", the Maritime Rescue co-ordination Center said in a statement.
The accident struck close to the Kerch Strait, which has become a new flashpoint in tensions between Russian Federation and Ukraine.
Maritime traffic was not affected by the incident and navigation through the Kerch Strait is still open, the director of the Crimean Sea Ports said.
The strait lies off Ukraine's Crimea peninsula, which Russian Federation annexed in 2014.
Three vessels from Kiev were seized in a major incident a year ago, reigniting fears of open conflict in the Black Sea.
In November 2018, Russian Federation captured three Ukrainian navy vessels and detained their crews, which sparked tensions between the two countries. Russian Federation annexed Crimea from Ukraine in 2014.
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