Blaze erupted as fuel was being pumped between vessels, says Russian government.
The Federal Agency for the Sea and River Transport said the blaze erupted while fuel was being pumped from one vessel to another. The fire spread from one ship to the other, prompting crews to jump overboard, according to Russian news agencies.
Media quoted the federal agency as saying the vessels, the Maestro and the Candy, had 31 crew members, who were citizens of Turkey and India.
The maritime agency said that salvage teams saved 12 crewmembers, correcting its earlier report that 14 sailors had been rescued.
It said that 11 bodies were taken from the sea, adding that rescuers saw another three dead but failed to recover them. The remaining five members of the crew were unaccounted for.
The Russian navy has joined the rescue operation, deploying two of its ships.
The fire erupted while the two vessels were near the Kerch Strait, which runs between Russian-annexed Crimea and southern Russia, and controls access to the Azov Sea from the Black Sea.