Russian gas monopoly Gazprom said full supplies are being restored to European countries, with many reporting back to normal levels.
"The work of restoring supplies is almost finished and Gazprom fulfils all its obligations to European consumers," said Sergei Kupriyanov, spokesman for the Russian state-controlled energy firm.
"Gazprom is compensating for the illegal siphoning-off of gas but will not be able to do this forever," he added, accusing Kiev of "continuing to steal" gas destined for western Europe.
But Ukraine said it was only taking gas it bought from Turkmenistan from the pipelines crossing its territory.
Talks due to begin
Executives from Ukraine's state-owned Naftogaz energy company are travelling to Moscow for talks with Gazprom to resolve the crisis between the neighbours.
Gazprom shut off gas supplies to Ukraine on Sunday after Kiev refused to accept a fourfold price rise.
EU officials are also expected to discuss the crisis in Brussels on Wednesday.
The European Commission, the bloc's executive arm, called on both sides to continue negotiations, with the dispute threatening to affect gas supplies across Europe.
Late on Tuesday the Ukrainian government said it sent a letter to the president of the EU commission, Jose Manuel Barroso, asking him to send experts to observe the gas flows in Ukraine's pipelines.
This follows comments earlier in the day by the Austrian EU presidency, who said the bloc would not play the role of mediator in the standoff and that a solution must be negotiated between Russia and Ukraine.
Europe imports a fifth of its natural gas from Russia through Ukraine, and analysts across Europe have noted Moscow's potential to wield vast energy supplies for political purposes.
Ukraine has claimed the gas price rise and subsequent shutoff is punishment for its attempts to become more independent of Moscow and develop stronger ties with the West.
Oil price rise
The dispute has caused world oil prices to rise, with New York's main contract, light sweet crude for delivery in February rising 21 cents to US$61.25 per barrel in electronic trading compared with Friday's close.
In London, the price of Brent North Sea crude for February delivery gained 37 cents to $59.35 per barrel compared with Friday's close.
Gazprom is still charging low prices for gas to some former Soviet countries, and said it would continue providing Ukraine with these if it handed control of the export pipeline to Russia.
With its 48 million people braced for shortages, Ukraine accused Moscow of putting "economic pressure" on Kiev and analysts said Russia was punishing Ukrainians for electing pro-Western President Viktor Yushchenko last year after the peaceful so-called orange revolution.