"It is very important that for the past year, we...have managed to carry out constructive work and build mutual understanding. In my view, we can already say that we have removed all of the gas problems," Tymoshenko said at a meeting with her Russian counterpart Vladimir Putin.
"At the very least, we are on the path to having no problems in this field," she added.
Russia, which supplies around one quarter of Europe's gas, briefly shut down supplies via Ukraine's pipeline system at the start of the year during a dispute over Kiev's debt for supplies. Ukraine transits around 80% of Russia's Europe-bound gas.
Tymoshenko said on Tuesday after talks with Putin that Russia and Ukraine had agreed that Kiev will only pay for gas it actually consumes. Gas contracts usually stipulate that the supplier is paid for what is ordered rather than what is actually consumed.
The two premiers are in Poland as part of events to commemorate the 70th anniversary of the start of World War II.
Tymoshenko also invited Putin to a session of an interstate commission on economic cooperation, due to take place in October in Kharkov, eastern Ukraine.
Putin said Russia and Ukraine had good prospects for cooperation in energy, aircraft building and a number of other branches.
"Attention is traditionally focused on the energy industry, but besides this there are other fields of interaction," he said.
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