Vladimir Putin said Russia could meet Ukraine 'halfway' on gas agreements
Russia has agreed to ease the terms under which it supplies gas to Ukraine, in a deal which Moscow says should prevent disruption in coming months.
The deal was announced after talks between Russian Prime Minister Vladimir Putin and Ukraine's Yulia Tymoshenko.
It means Ukraine will not be fined for using less gas than in its current contract, because of the downturn.
In January, many countries in Europe were left short of gas due to a payment dispute between Moscow and Kiev.
Russia provides about a quarter of the gas consumed in the EU and 80% of that is piped through Ukraine.
The two prime ministers met in the Ukrainian resort town of Yalta on Thursday to discuss the issue of gas supply.
Under contracts signed with Russia earlier this year to end last winter's dispute, Ukraine faced the prospect of huge fines if it did not pay for all the gas it had contracted to buy, regardless of the amount actually used.
A dispute between Russia and Ukraine in January cut supplies to Europe
Gas consumption in Ukraine has dropped sharply as a result of the economic crisis.
Mr Putin said Gazprom and Naftogaz, the two countries' energy firms, would agree on new volumes.
"We deemed it possible to meet Ukraine halfway and tweak several of our earlier agreements," Mr Putin said.
In a reference to January's dispute, he added: "It would be very good to meet the New Year without any calamities."
Ms Tymoshenko played down the prospect of further disruptions to Europe's gas supply, pledging that Ukraine would meet its obligations to Russia.
"Ukraine has been paying and will continue to pay on time," she said.
In August, the EU and international lending institutions agreed a $1.7bn (£1bn at the time) loan deal for Ukraine to help secure European gas supplies, in return for reforms to Ukraine's gas sector.