Pipes across Ukraine carry about a fifth of the European Union's gas needs
Russian PM Vladimir Putin has told gas giant Gazprom to cut supplies sent via Ukraine to Europe over allegations Kiev is siphoning some off.
Mr Putin said flow should be reduced by the amount Ukraine had taken since deliveries ended on 1 January.
Russia stopped supplying gas to Ukraine five days ago amid a row over unpaid bills and a new pricing contract.
Ukraine denies siphoning off gas and says technical problems are disrupting the flow.
Pipes across Ukraine carry about one-fifth of the European Union's gas needs.
Several EU countries have reported a drop in gas deliveries since 1 January, apparently as a result of the dispute.
The move came after Mr Putin held talks with Gazprom CEO Alexei Miller.
Mr Miller recommended that deliveries via Ukraine should be reduced "by the amount stolen by Ukraine, that is 65.3 million cu/m of gas".
Future deliveries should be reduced on a daily basis by the amount of gas stolen, he added.
Gazprom said it would compensate by sending more gas to Europe via other routes.
Earlier, EU Commission spokesman Ferran Tarradellas said there was no immediate danger to EU consumers or industry.
The cut-off had produced "some irregularities" but "no substantial disruption of supply to any member state", he said.
Among the countries to have reported falling pressure in their pipelines are Poland, Hungary, Bulgaria, Romania, the Czech Republic and Greece.
In some cases supplies dropped by as much as 30% - but countries are compensating by using their own reserves or increasing deliveries from other sources.
The row between Russia and Ukraine has been simmering for weeks. Gazprom says Ukraine owes it money; Ukraine says it has paid its debt. The two sides have also failed to agree on the price Ukraine should pay for gas in 2009.
A similar row between Gazprom and Ukraine at the beginning of 2006 led to gas shortages in several EU countries.
EU leaders have been meeting in Brussels to discuss the dispute and a delegation has also been sent for talks with both Ukrainian and Gazprom officials.
But, say correspondents, the EU is reluctant to get involved in what it describes as a commercial dispute - reflecting Europe's own deep divisions on how to respond to Russia.
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