Spokesman Sergei Kupriyanov said after talks in Kiev that Russia would switch to an advance payment system if it did not receive the money, meaning Moscow could cut off gas supplies to Ukraine.
Cutting supplies could disrupt the gas flow to the European Union, reports Reuters.
“The talks in Kiev finished around 2:30 a.m. Moscow time (22:30 GMT on Sunday). The Russian side is expecting payment of the accumulated gas debt of $1.951 billion before 10 a.m. (06:00 GMT) on June 16,” Kupriyanov said.
“If the funds are not paid, gas supplies will, as was announced earlier, be switched to a pre-payment system.”
Russia and Ukraine disagree how much Kiev should pay for the natural gas it receives from Russia.
European Energy Commissioner Günther Oettinger told reporters in Kiev that he had made a compromise proposal during talks which began late on Sunday but Moscow had declined the offer.
Prospects of a breakthrough had dimmed because of political tensions and clashes between government forces and pro-Russian separatists in east Ukraine.