European consumers were left in the cold for weeks in January 2009 when Russian gas monopoly Gazprom cut gas shipments to Ukraine because of payment and contract disputes. Most of Russia's gas for Europe runs through Ukraine's gas transit system.
Kiev brokered a gas deal with Gazprom earlier this year in exchange for an extended lease for the Russian Black Sea fleet in Crimea.
Sergei Tigipko, Ukraine's deputy prime minister, was quoted by the Platts news service as saying improved relations lowered the possibility of a gas crisis during the coming winter.
"I hope that this December there will be no problems and Europeans have no (grounds) to worry over the transit of Russian gas via Ukraine, contrary to what had happened (in the past)," he said.
Moscow has moved to diminish Ukraine's role as a gas transit nation for Europe with its Nord Stream and South Stream gas pipelines. Both projects would move Russian gas to Europe while avoiding Ukrainian territory.