The fire broke out when one vessel was transferring fuel to the other, driving both crews to jump overboard, said Mr Kravchenko.
Between eight and ten ships have been sent to the rescue and are picking up the sailors, the emergency services said.
Twelve people have been saved, Russia's Federal Agency for Sea and River Transport (Rosmorrechflot) told the Moscow-based Interfax news agency.
Clouds of black smoke can been seen billowing from one of the ships has a huge fire burns through the deck.
The fire occurred on two ships, the Candy (or Kandy) and the Maestro, flying the flag of Tanzania, at 18:00 Moscow time on January 21.
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The ships involved were the Kandy, with a crew of 17, and the Maestro, with 14 on board.
The accident struck close to the Kerch Strait, which has become a new flashpoint in tensions between Russian Federation and Ukraine.
A Russian-built bridge over the Kerch Strait opened in May previous year. Russian Federation has moved to seize the worldwide waterway following its annexation of the adjoining Crimea Peninsula in 2014. Ukraine has alleged that ships that want to sail on to Ukrainian harbors are hassled by Russian authorities.
In November 2018, Russian Federation captured three Ukrainian navy vessels and detained their crews, which sparked tensions between the two countries.