RFE/RL's Belarus Service is reporting that officials in Minsk have apparently cancelled the oil-transit fees imposed on January 1.
Moscow had refused to pay, and said it would not resume negotiations until the duty was scrapped.
Russia cut off supplies on January 8, accusing Belarus of illegally siphoning off Russian oil destined to Europe.
A 'Lengthy' Conversation
The Belarusian presidency said in a statement that the compromise was reached during a "lengthy" telephone conversation today between Lukashenka and Russian President Vladimir Putin.
It said the prime ministers of the two countries have been instructed to work out concrete proposals to end the dispute and present them to Lukashenka and Putin on January 12.
The Kremlin press service confirmed the telephone conversation took place at Lukashenka's request.
But the Kremlin made no mention of a deal, saying that simply that the presidents discussed "questions of economic cooperation, including in the energy sphere, among them problems with the transit of Russian oil through Belarus."
EU leaders have strongly criticized the shutdown of the Druzhba pipeline, which carries about 10 percent of the European Union's oil needs.
The dispute has disrupted oil supplies to supplies to Ukraine, Germany, Poland, Hungary, the Czech Republic, and Slovakia.
European Worries
Speaking to a news conference in Brussels today, European Commission President Jose Manuel Barroso reasserted the need for Europe to develop alternative energy sources.
Barroso speaking in Brussels today (epa)