The warning is the latest skirmish in the long-running dispute between Moscow and Kiev over gas.
Russia, which supplies a quarter of Europe's gas, has twice cut off supplies in mid-winter in recent years due to pricing disputes with Ukraine, leaving parts of Europe without heating.
Last week, the two sides failed to agree how Ukraine's underground storage facilities would be filled and who would pay for this. Ukraine, whose economy has been slammed by the global crisis, proposed deferring payments of up to $5 billion it needs to pay for the gas to be stored underground.
In a statement Tuesday, Gazprom's CEO Alexey Miller warned that Ukraine might be required to prepay its bills in their entirety if it falls behind in its payments to Russia.
"Naftogaz Ukrainy is finding it enormously difficult to pay its bill for May," Gazprom spokesman Sergey Kupriyanov said in the statement.
Gazprom also said it wants to store extra gas in Ukraine during winter to be able to respond quickly to the needs of its customers in Europe.
Russia called on the European Union last week to help Ukraine pay its gas bill and help avert a new gas war.
Naftogaz and Ukraine's Fuel and Energy Ministry declined to comment on the Russian accusations.
However, Oleksandr Hudyma, energy adviser to Prime Minister Yulia Tymoshenko said that Gazprom's warnings were aimed at pushing the European Union to drop plans to help upgrade Ukraine's gas transit system. He asserted Moscow was trying to push the EU into endorsing or investing in Russia's efforts to build supply routes that bypass Ukraine-the North and South Streams.
"They are putting pressure ... not on Ukraine, but at the European Union," he said.
Hudyma said the warnings from Moscow were also aimed at supporting Gazprom's business. He said the statement was aimed at persuading the European Union to loan Ukraine money so that Kiev would continue purchasing Russian gas.
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