Russian and Ukrainian gas officials are meeting to discuss a row over gas prices, which led to a disruption of supplies across Europe.
Russia usually supplies 30% of Ukraine's gas
Russian gas giant Gazprom says full supplies are being restored to European states, and Austria and Hungary have reported a return to normal levels.
Gazprom has repeated claims that Kiev is stealing gas intended for Europe.
But Ukraine says it is only taking gas it bought from Turkmenistan, from the pipelines crossing its territory.
Gazprom stopped exporting gas to Ukraine on Sunday, after Ukraine refused to accept a rise in price from $50 to $230 for 1,000 cubic metres, but left enough in the pipeline for other customers.
Delegates from Ukrainian state energy company Naftogaz are holding talks with Gazprom executives, while EU energy officials are set to discuss the crisis on Wednesday.
EU energy commissioner Andris Piebalgs said the current situation showed how vulnerable the EU was to shortages of gas.
Kiev has denied any wrongdoing and says it is being punished for its attempts to become more independent from Moscow and develop stronger ties with the West.
On Tuesday, a Naftogaz representative, Mykola Goncharuk, said Ukraine had been taking Turkmen gas from the pipeline network.
However, Russian Industry and Energy Minister Viktor Khristenko said Russia was now buying all the Turkmen gas that entered the pipelines leading from Russia to Ukraine.
"The gas which arrives on Russian territory is Gazprom's gas, which... it supplies to Europe," he said, quoted by Interfax.
"Ukraine is continuing to steal," Gazprom spokesman Sergei Kupriyanov told reporters.
Mr Goncharuk repeated Ukraine's claim that existing contracts allow it to take a share of Russian gas exported via the Ukrainian pipeline in lieu of a transit fee, and said it would do so if the temperature fell well below freezing.
Moldova cut off
Gazprom is still charging low prices to some former Soviet countries, and has said it would give the same preferential treatment to Ukraine if it gave Russia control of the export pipeline.
Moldova says it was also cut off after refusing to double what it paid to $160 for 1,000 cubic metres.
Poland, which has had its gas supplies disrupted, said on Tuesday that it was looking for alternatives to Russian energy supplies.
Relations between Russia and Ukraine have been tense since President Viktor Yushchenko came to power last year on a promise to strengthen relations with the EU and Nato, and steer the country out of Russia's sphere of influence.
Ukraine says it is not opposed to an increase in gas prices, if it is phased in gradually.