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Yulia Tymoshenko, Ukraine's prime minister. YALTA, Ukraine -- Russian Prime Minister Vladimir Putin promised Thursday to give struggling Ukraine a break by altering tough conditions in a natural gas contract, a move that could ease European supply concerns and give Putin's counterpart Yulia Tymoshenko a boost amid a bitter presidential campaign.

Tymoshenko assured Putin that Ukraine will meet its obligations as a transit country for Russian gas piped to Europe.

The prime ministers met in the Crimean resort of Yalta amid tension between their nations over energy and recriminations in Ukraine's riven leadership ahead of a Jan. 17 presidential vote. The volatile atmosphere has led to European fears of a repeat of last winter's disruption of Russian gas supplies via Ukraine, cut off for two weeks amid a price dispute between Moscow and Kiev.

Putin and Tymoshenko ended the supply drought last January by forging a new gas deal, but it obliges Ukraine to pay in full for contracted gas volumes regardless of the amount used - a provision that has become a powerful weapon in Moscow's hands as Ukraine has drastically cut consumption this year amid a severe economic crisis.

But Putin said Thursday that the main Russian and Ukrainian gas companies would revise the contracted volumes to ensure that Ukraine would not have to pay fines.

"Gazprom and Naftogaz will agree on new volumes," Putin said, adding: "If there is no surplus of volume, there will be no sanctions."

Putin's government had already said it would not exercise its right to fine Ukraine over volumes, but has not formally abandoned the provision. Observers have interpreted the Russian promise to go easy on Ukraine as a gesture of support for Tymoshenko, who is running for president and has faced sharp criticism over the gas deal.

Tymoshenko thanked Putin for the gesture, expressing gratitude that "you, as a strong country, are meeting us halfway, taking into account the crisis conditions."

She also said Ukraine will not jeopardize Russian gas supplies to Europe, and will pay on time for the gas that fuels its own economy.

"Ukraine has been paying and will continue to pay on time," Tymoshenko said. "In addition, we will continue to diligently and correctly fulfill our duties on gas transit."

Putin has warned European countries that Ukraine may not be able to meet its commitments to Russia's state-controlled gas monopoly Gazprom and urged the European Union to lend Ukraine at least $1 billion to help it pay.

EU nations receive 20 percent of their gas from Russia, most of it via pipelines crossing Ukraine.

Tymoshenko's rival, President Viktor Yushchenko, has sharply criticized her January gas deal with Russia, saying it betrayed national interests. He urged Russia on Thursday to re-negotiate the contract, warning in an open letter addressed to President Dmitry Medvedev that the failure to do so could jeopardize the gas deliveries to Europe via Ukraine next spring.

Russia responded angrily, with a top Kremlin aide calling the warning "blackmail."

Putin's promise to agree on lower gas volumes should take some of the punch away from the pro-Western Yushchenko's criticism of Tymoshenko. Putin avoided any mention of Ukraine's presidential campaign, but praised Tymoshenko's government as efficient and a force for stability.

"We work comfortably with the Tymoshenko government," he said.

Putin supported Yushchenko's unsuccessful rival in the 2004 Ukrainian presidential election, Viktor Yanukovych, and Russia has essentially severed relations with the Ukrainian president. Yushchenko is seeking re-election but polls show him lagging far behind front-runners Tymoshenko and Yanukovych, both of whom have been much more friendly to Moscow.