The fire broke out on Monday off Russia's territorial waters.
Another 12 people have been saved as the rescue operation is ongoing. One of the ships was reportedly rocked by a blast.
Ukraine condemned the Russian move, denying that its ships had violated the navigation laws in the area. Nine sailors are still listed as missing, the spokesperson said. Fourteen people have so far been rescued.
The BBC reported that one of the vessels, the Kandy, carried 17 crew members while the Maestro with 14 crew members. Turkey confirmed that 16 of its citizens were aboard the affected vessels.
The explosion happened while the two vessels were sailing in neutral waters near Ukraine and Russian Federation.
Severe weather conditions at sea have prevented rescue ships from taking victims to the shore for medical treatment, the report added.
The violation of safety rules during the fuel transfer from a tanker to the other vessel is said to be the cause behind the incident, according to one of the preliminary theories.
The Kerch Strait, located between Russian-annexed Crimea and southern Russia, controls access from the Black Sea to the Azov Sea, which has Ukrainian and Russian ports.
The accident struck close to the Kerch Strait, which has become a new flashpoint in tension between Russian Federation and Ukraine.
Three vessels from Kiev were seized in a major incident previous year, reigniting fears of open conflict in the Black Sea.
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