The Commission's chief spokesman Johannes Laitenberger said the European Union would look into whether it could do business as usual with the former Soviet republics if they did not settle their row at the weekend or by early next week.
"The European Commission believes that the meetings in coming days offer the last and best chance for Russia and Ukraine to demonstrate they are serious about resolving this dispute," Laitenberger said.
"We will regard this period as a test case for judging whether or not they are credible partners," he said.
The Russian and Ukrainian premiers, Vladimir Putin and Yulia Tymoshenko, are to meet in Moscow on Saturday to try to resolve the row, which has affected households and industries in 18 EU countries. Russian President Dmitry Medvedev has proposed a meeting with gas importers in Moscow for the same day.
Kiev and Moscow have been embroiled in a bitter dispute over debt and gas prices for Ukraine in 2009, which resulted in the suspension of deliveries to Ukraine on January 1. A week later, Gazprom cut off supplies to Europe via Ukraine, accusing Kiev of stealing gas intended for EU consumers. Ukraine has denied the accusation.
The crisis has seen an increase in discussions in Europe about the need to diversify supplies. The European Union buys a quarter of its gas, transited mainly via Ukraine, from Russia.
Russia's energy giant Gazprom again blamed Ukraine on Friday for blocking the supplies.
"Gazprom is again calling on Naftogaz to stop looking for excuses for its unwillingness to resume transit to Europe and to turn on the taps [on gas pipelines] on its territory," the company said in a statement, adding that its taps have been turned on for the past four days.
The gas monopoly said it had repeated its request to Naftogaz to allow the flow of 92.2 million cubic meters of gas a day via Ukraine at 2:00 p.m. Moscow time (11:00 a.m.).
"Naftogaz answered in the negative, rejecting its own proposal [on the volume of gas] made a few hours earlier, again citing the lack of an agreement on receiving gas at transit points," the company said.
An EU-brokered deal to have Russia's Europe-bound supplies restarted on Tuesday without a bilateral contract with Ukraine fell through, even though international monitors were deployed to ensure gas would not be siphoned off while in transit.