The countries' presidents "discussed Russian-Belarusian economic cooperation, including energy problems and Russian oil transit through Belarusian territory," the press service said adding that the conversation was initiated by Lukashenko.
Russia halted crude supplies via its western neighbor on Sunday, accusing Belarus of siphoning Europe-bound oil from the Druzhba (Friendship) pipeline.
The press service of the Belarusian president said Minsk and Moscow have reached a compromise on the issue.
"A compromise has been found which will help break the deadlock, including over the transit of Russian oil to European countries via Belarus," the press service said.
It also said the countries' prime ministers have been instructed to draw up solutions to the standoff by January 12.
The dispute began when Moscow doubled the price for natural gas it supplies to its ex-Soviet neighbor to $100 per 1,000 cubic meters as of January 1, and imposed an oil export duty of $180.7 per metric ton. Belarus, whose economy was set to be hard hit by the charges, retaliated January 3 by introducing a transit fee of $45 per metric ton for crude passing through its territory to Central Europe.
Druzhba, one of the world's largest pipelines, passes through European Russia to Belarus, where it divides into two branches. The northern branch supplies Poland and Germany, and the southern route passes through Ukraine, to Hungary, the Czech Republic, and Slovakia.
Poland and Germany announced Monday that Russian crude supplies through the pipeline were disrupted. Russia's pipeline monopoly Transneft said it had halted supplies as of Sunday morning, due to Belarus's tapping of Europe-bound crude.
Russia currently exports some 20% of its oil via the Druzhba pipeline, and the loss of that route could leave Russia with an oil surplus.