Hundreds of thousands of Europeans have been without gas for a week
The EU has told Russia it is disappointed that little gas has flowed into Europe from Ukraine, despite an agreement to resume deliveries.
European Commission President Jose Manuel Barroso said only limited access was given to EU officials monitoring Russia and Ukraine's gas network.
Moscow said it had resumed gas supplies into Ukraine early on Tuesday, but Kiev was refusing to pass the gas on.
Ukraine blamed Russia for changing the delivery route.
The dispute dashed hopes of ending a row which has hit several countries' supplies, leaving hundreds of thousands of Europeans without gas for a week.
Moscow has been unable to resolve differences with Ukraine over debts and pricing.
Lack of trust
EU monitors confirmed a "very limited" amount of gas started flowing from the Russian pumping station at Sudzha on Tuesday morning.
Mr Barroso telephoned Russian Prime Minister Vladimir Putin to express disappointment at the low levels of gas, as well as the apparent lack of access to dispatch centres for EU monitors.
Mr Barroso said he would also discuss the problem with the Ukrainian leadership.
Mr Medvedev said Gazprom had informed the European Commission it was unable to supply gas through Ukraine because Kiev had not opened any export pipelines.
"Ukraine didn't open the route for gas transit," he said. "If the system is closed, we can't provide gas."
Ukrainian gas company Naftogaz demanded "the immediate resumption of even supply of gas along all transit routes", saying the amount and direction of the gas had not been agreed by the two sides.
Gazprom deputy head Alexander Medvedev said Ukraine had failed to carry the gas onwards to Europe after it resumed pumping it across their border.
Ukrainian President Viktor Yushchenko called on Russia to "stop the blackmail" and work out an agreement.
The BBC's Rupert Wingfield-Hayes, at a pumping station on the Russian-Ukrainian border, says the latest twist in the dispute is symptomatic of the total lack of trust between the two countries.
Russia cut gas supplies to Ukraine on New Year's Day, saying it would pump only enough for customers further down the pipeline.
Moscow accuses Ukraine of siphoning off gas intended for third countries
But then Moscow accused Ukraine of siphoning off gas intended for third countries.
Ukraine denied the claim, but the flow of Russian gas ceased completely on 7 January, leaving many European countries with major shortages.
In a deal reached on Monday, Russia agreed to resume supplies if Russian and EU observers were allowed to monitor their transit through Ukraine.
The move was designed to calm Russian fears that Ukraine was siphoning off gas for its own use.
The EU gets a quarter of its gas supplies from Russia - 80% of which passes through Ukraine - and more than 15 countries across central Europe have been hit by the shutdown of Russian supplies.
Wider gas network
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