"The subject has been exhausted. No one will have any claims against each other and no damages will be sought," Tymoshenko told 1+1 TV channel.
Deputy Gazprom CEO Alexander Medvedev said on Tuesday that the Russian energy giant could ask Kiev to pay for its losses following the gas conflict. He said the unsanctioned gas siphoning had been registered and Gazprom had the right to demand compensation.
Russia had earlier accused Ukraine of stealing gas intended for EU consumers and said its financial losses were estimated at more than $1.2 billion.
Gazprom and Ukrainian energy company Naftogaz finally signed on Monday a contract on Russian gas supplies to Ukraine for 2009-2019. The first gas started to flow on Tuesday.
Tymoshenko hailed the resolution to the dispute as a victory for Ukraine, but President Viktor Yushchenko and his office have criticized the deal.
Yushchenko is convening the National Security and Defense Council on Friday to discuss the gas deals with Russia. Tymoshenko declared on Wednesday that there was no way the council could revise the agreements.
