The office said that Vladimir Putin, Russia's president, and Alexander Lukashenko, the Belarus president, had ordered their prime ministers to work out a package of measures to resolve the dispute.
These would be submitted for approval by the two leaders on Friday.
On Monday, Russia stopped pumping oil to Europe via the Druzhba, or Friendship, pipeline that crosses Belarus, accusing its neighbour of siphoning off oil.
By Tuesday, the stoppage had affected supplies to Ukraine, Germany, Poland, Hungary, the Czech Republic and Slovakia.
The oil shortages have caused more damage to Russia's reputation as a key energy supplier to the European Union (EU), one year after a price dispute with Ukraine led to a brief interruption of EU gas imports from Russia.
EU leaders have strongly criticised the shutdown of the oil pipeline.
The dispute centres over Russia's decision to impose a significant duty on oil exports to Belarus, with Moscow complaining that the previous duty-free regime has been costing the Russian budget up to $4bn a year.
Minsk's government, which is tied to Moscow through a loose union treaty and relies on cheap Russian energy and duty-free trade with Russia, hit back by putting duties on Russian oil pumped across Belarus to Europe.
Putin took a harsh stance at a cabinet meeting on Tuesday, ordering his government to work out a set of punitive measures aimed at Belarus to protect the national economy.
Talks between Belarus and Russia broke up in failure on Tuesday after Moscow insisted that Minsk drop the oil transit fee.
Vedomosti, the Russian business newspaper, reported on Wednesday that Russia was planning to impose duties on more than half of Belarusian imports.