After a phone call with Putin, President Alexander Lukashenko said that the compensation could amount to $300 million.
"It was an unexpected proposal," Lukashenko said, adding that Putin also offered to keep oil supply terms at last year's level.
Belarus said it lost $330 million in 2019 due to changes in Russian taxation, Presstv Reported.
Under a duty-free deal between Russia, Belarus and Kazakhstan, Russia used to send crude oil and oil products to the capital Minsk with no export fee.
Moscow, however, amended its tax code in January last year to halt that arrangement.
Kremlin spokesman Dmitry Peskov, however, said on Friday that the two sides have not reached any firm agreement on the terms of oil supplies.
While Moscow and Minsk had been on loggerheads over the agreement, the US, which has long been criticizing Minsk for what it called “authoritarian rule” was trying to “normalize” ties with Minsk.
In a visit to the country earlier this month, Secretary of State, Mike Pompeo, claimed that Washington supported the independence of Belarus while being aware of Minsk’s longstanding ties to Russia.
“There’s a long history with Russia. It’s not about picking us between the two. We want to be here,” he added.
Pompeo said that Washington will also appoint a new ambassador to Minsk soon.