Chief executive Alexei Miller said it was now certain that Ukraine would pay its $300 million bill for June.
"No one wants the crisis to be repeated. That was an anomaly," Miller told reporters following talks with Ukraine's officials, in a much more conciliatory comment than in previous days.
Belarus, which is the second-most important route for Russian gas to Europe after Ukraine, also said it would begin paying gas arrears to Russia from July.
Gazprom, Naftogaz Ukrainy, global banks and the European Commission are to hold talks Monday to find a way to help Ukraine fill its gas storage to ensure smooth supplies during the winter.
Miller said he hoped that a compromise would be found to help Ukraine raise the funds, as the country wants to step up imports from July and onward to take advantage of falling gas prices. Ukraine says it needs $4 billion to fill gas storage.
Under a 10-year deal signed in January that ended a two-week cutoff of supplies to Europe, Ukraine must pay by the seventh day of the month following the imports.
With Belarus, the rules are less strict, but Moscow revealed this month that Minsk owes $230 million and demanded quick repayment. Miller said the debt was $244 million and said the contract foresees arbitration or supply reduction, though he said he was confident that a compromise would be reached.
Belarussian First Deputy Prime Minister Vladimir Semashko said Minsk would repay gas arrears before the end of 2009.
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