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.
European Commission president Jose Manuel Barroso telephoned Russian Prime Minister Vladimir Putin to express disappointment at the low levels of gas flowing from Russia and at the apparent lack of access to dispatch centres for EU monitors, EU officials said.
Mr Barroso said he would also discuss the problem with the Ukrainian leadership.
Russia shut off the gas to Europe last Wednesday, accusing Kiev of stealing gas meant for other European customers.
Ukraine didn't open the route for gas transit - if the system is closed, we can't provide gas
However, 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.
Russia said gas started flowing from the Russian pumping station at Sudzha at 1030 local time (0730 GMT) on Tuesday.
This was later confirmed by EU monitors, although the amount of gas, they said, was "very limited".
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. The Ukrainian side cynically informed us that the gas transport system had been reoriented to domestic consumers.
"We don't know what to do at the moment."
Thousands of Europeans have been left without gas in freezing temperatures
After the gas was switched on at Sudzha, 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.
Mr Yushchenko, speaking in a televised press conference later on Tuesday, said: "Each person living in Ukraine should understand that what has happened between 1 January and now is not the blackmail of our state, it is the blackmail of each of you."
He went on: "What is most important in these talks now is to bring a halt to the political emotions, stop the blackmail and let experts start working out answers [for transit and supply contracts]."
Russia cut gas supplies to Ukraine on New Year's Day, saying it would pump only enough for customers further down the pipeline.
But then Moscow accused Ukraine of siphoning off gas intended for third countries and it restricted supplies even further.
Ukraine denied the claim, but the flow of Russian gas ceased completely on 7 January, leaving many European countries with major shortages.
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.
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