"There are 11 bodies," Alexei Kravchenko, spokesperson for Russia's Federal Agency for Maritime and River Transport, told AFP.
"Another three people went under water before rescue workers' eyes."
Those three are most likely dead, he said.
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The ships, the Kandy and the Maestro, had crews of nationals from India and Turkey.
At least 11 killed after two ships catch fire in Kerch Strait https://t.co/mvEnNIU6NT pic.twitter.com/UonQWMd560
— CGTN (@CGTNOfficial) January 22, 2019
The Kandy had a 17-strong crew, while the Maestro carried 14 people.
Twelve people had survived, Kravchenko said, but "no one knows where the other five people are".
The fire broke out when one vessel was transferring fuel to the other, driving both crews to jump overboard, said Kravchenko.
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"A search-and-rescue operation is continuing," Kravchenko added.
Authorities in the Crimean city of Kerch were preparing to receive the victims, he added.
The accident struck close to the Kerch Strait, which has become a new flashpoint in tensions between Russia and Ukraine.
In November, Russia fired on and seized three Ukrainian navy vessels in the Kerch Strait as they tried to pass from the Black Sea to the Azov Sea.
The confrontation was the first open military clash between Kiev and Moscow since 2014, when Russia annexed Crimea and a pro-Russian insurgency erupted in eastern Ukraine.
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