KIEV - Ukrainian state energy firm Naftogaz said on Tuesday Russia had agreed to a 30 percent increase in the transit tariff for the oil it transports to Europe in a deal that calmed fears of supply cuts.

Russia said on Monday it had agreed terms for a new oil deal with Ukraine a few hours after spooking Europe with a warning the continent could face oil supply cuts because of a dispute between Moscow and Kiev.

The rate has been increased by 30 percent, a Naftogaz spokesman said. There will be no crisis. We signed an agreement last night.

I confirm the fact of the signing, Russian spokeswoman for the energy ministry said.

Europe, which receives much of its oil and gas from Russia, has closely tracked disputes between Russia and its neighbours after EU gas supplies were cut in the dead of winter in 2006 and 2009 due to rows between Russia and Ukraine.

I am also very glad to note that the Russian and Ukrainian sides have meanwhile found an agreement avoiding a disruption of oil supplies to the EU, EU Energy Commissioner Andris Piebalgs said in a statement.

Naftogaz did not specify the tariff Russia had agreed to pay. But a government source told Reuters the tariff will be 6.6 euros ($9.50) per tonne of oil for the entire journey through Ukraine in 2010 against $7.8 this year.

Ukrainian officials have said switching to euro payments from the dollar had been one of their demands.

The source also said Kiev and Moscow had agreed that the volume of oil -- going amongst others to Slovakia, Czech Republic and Hungary -- will be 15 million tonnes next year.

Russia transported 17.1 million tonnes of oil in 2008. The figure for this year is as yet unknown. (Reporting by Pavel Polityuk; writing by Sabina Zawadzki; editing by James Jukwey)