According to the BBC Russia accused Ukraine of targeting the Arctic Metagaz with "uncrewed sea drones" launched from the Libyan coast.
Ukraine's SBU state security service has not commented on the allegation and the Libyan port authority said the cause of the fire was unclear.
The Libyans said the tanker was carrying about 62,000 tonnes of LNG before the blasts and that it sank about 130 nautical miles (240km) north of the Libyan port of Sirte.
Russia's transport ministry said 30 Russians were aboard the Arctic Metagaz. Maltese Home Affairs Minister Byron Camilleri said they were all found "safe and sound in a lifeboat" during a rescue operation by Malta's armed forces.
Unverified night-time footage has emerged purportedly showing the ship ablaze after the attack, which occurred on Tuesday.
Serhii Sternenko, a popular blogger and adviser to Ukraine's defence minister, posted pictures on Wednesday morning of what he said was the tanker in the Mediterranean, which had a "serious hole in the engine room compartment and is beyond repair".
He did not elaborate where the pictures came from and they have not been independently verified.
"This is a terrorist attack," Russia's Vladimir Putin told state TV. "This isn't the first time we've encountered something like this."
Russia's transport ministry called it "an act of international terrorism and maritime piracy", singling out the European Union for complicity.
Moscow said the Arctic Metagaz - which had been en route from Russia's northern port of Murmansk - was carrying cargo cleared in accordance with international rules.
The tanker was apparently heading for Port Said in Egypt and is considered part of Russia's so-called shadow fleet. It has been widely sanctioned by Western countries.
The ministry provided no evidence to back up its claim that the tanker was attacked by Ukrainian sea drones, though there were earlier unconfirmed reports of attacks from the Libyan coast.
The SBU told BBC Ukraine it was not commenting on "the situation with the tanker in the Mediterranean", although a Ukrainian government-linked social media account, United24, teased that the drones were "Definitely. Maybe" not part of the Ukrainian fleet.
