Russian Prime Minister Viktor Zubkov told Tymoshenko at a meeting that full payment of the debt will pave the way for the two countries to reach an agreement for long-term gas cooperation, "eight to ten years ahead."
Tymoshenko said: "Resolving all issues in the gas sector is a serious achievement. Ukraine has paid off all its commitments."
Ukraine, which transits about 80% of Russia's Europe-bound gas, threatened to start tapping fuel after Russia halved shipments to the country amid a dispute over Kiev's gas debt and supply scheme earlier this year.
European consumers did not report any shortfalls in supplies, however, unlike at the start of 2006, when a bitter pricing row led Moscow to briefly cut off deliveries to its ex-Soviet neighbor.
Moscow and Kiev resolved their fresh gas dispute in mid-March, agreeing on the size of the debt and a supply scheme, although some issues still need to be addressed.
Zubkov said Russia and Ukraine should cooperate in the hi-tech sphere to be competitive on world markets. "Through joint efforts we will be able to ensure a worthy place for Ukraine and Russia in world labor division," he said.
Tymoshenko praised bilateral relations and said the Russian and Ukrainian governments had drafted a joint action plan. She said bilateral trade grew 28% for the first three months of 2008.