Russia last month rejected a Ukrainian proposal to defer payment on up to $5 billion in gas storage fees, barely four months after a January pricing dispute between them disrupted supplies to Europe.
Russia has urged the EU to help Ukraine pay the bills, and Barroso said he discussed the matter with Prime Minister Vladimir Putin by telephone Friday.
"Prime Minister Putin called me to tell me about the difficulties he anticipates in payments coming from Ukraine [and] to say that Ukraine has asked for some support for financing of these payments," Barroso told reporters.
"It is difficult with our budget, if not impossible, to have some support from the Community budget for Ukraine."
He said he had promised Putin that he would raise the matter with EU leaders who are due to meet June 18 and 19 in Brussels.
But he stressed that it was mainly a problem between Ukraine and Russia. Putin disagreed.
"We said we are ready to assume part of the responsibility and financial obligations in solving the problem," Putin said in a statement.
"But I want to stress that Russia is not going to carry alone the responsibility of subsidizing Ukraine's economy."
Putin said he had proposed to IMF Managing Director Dominique Strauss-Kahn that part of the $10 billion Russia seeks to invest in IMF bonds be used to help Ukraine. He did not specify how exactly this could be done.
"We are grateful to D. Strauss-Kahn for his initial positive reaction," Putin said.
Europe receives about one-fifth of its gas from Russia via Ukraine, with some eastern and southern European countries almost completely dependent on that gas.
Gazprom last week said it was concerned that Ukraine would not pay for this month's gas supplies in full. It said it would have to move to 100 percent advance payments if there were any disruptions.
Gazprom wants to store extra gas in Ukraine during the winter to be able to respond more quickly to the needs of its customers in Europe.
Italian Prime Minister Silvio Berlusconi, whose country is one of Europe's biggest consumers of Russian gas, has pledged to present to the EU summit a Russian proposal that Europe bear some of the costs that Ukraine is unable to meet.
The temporary cut of Russian gas supplies via Ukraine to Europe in January undermined European confidence in Russia as an energy supplier and has given extra urgency to the bloc's attempts to seek alternative fuel sources.
At a summit in Prague this month, EU leaders offered to provide more trade and stronger transport links to gas transit countries such as Turkey and Azerbaijan in return for them supplying gas through an alternative "southern corridor" route.
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