The United States cut off Venezuela's oil exports to Cuba after toppling Venezuelan president Nicolas Maduro on January 3, and US President Donald Trump threatened to slap punishing tariffs on any other country that sent crude to Cuba.
But Trump on Sunday signalled he was reversing course and expressed sympathy for the Cuban people's need for energy.
"If a country wants to send some oil into Cuba right now, I have no problem, whether it's Russia ... and if other countries want to do it," Trump told reporters aboard Air Force One.
"One boatload of oil, that's all it is," Trump added.
The Anatoly Kolodkin was waiting to offload at the port of Matanzas, Russia's transport ministry said.
The Kremlin said it had raised the issue of the tanker during talks with the US but that Russia felt it had a duty to support "friends" in Cuba.
"This issue was indeed raised in advance during contacts with our American partners," Kremlin spokesman Dmitry Peskov told reporters.
Cuba has not received an oil tanker in three months, according to President Miguel Diaz-Canel, and its energy crisis has caused blackouts across the country of 10 million.
Health officials say the crisis has increased the mortality risk for cancer patients, especially children.
Cuba became dependent on the Soviet Union for oil after its communist revolution in 1959, and needs imported fuel oil and diesel to generate power.
Asked if further Russian shipments would follow, Peskov said: "In the desperate situation that Cubans now find themselves in, this, of course, cannot leave us indifferent so we will continue to work on this."
LSEG ship-tracking data showed the Russian tanker had left the Russian Baltic Sea port of Primorsk on March 8 and was now moving along Cuba's northern shore.
with DPA
