Vladimir Putin's spokesman said that during the telephone conversation, the sides also discussed means of strengthening bilateral ties.
"Putin said that Russia wants to develop cooperation with its Ukrainian partners in all areas," Dmitry Peskov said.
Putin also congratulated Tymoshenko on her birthday.
Ukraine's national oil and gas company Naftogaz pledged on Wednesday to pay its $380 million debt to Russia for gas supplied in September by the weekend.
Russia has put Ukraine's debt at $2.4 billion, including fines and arrears. Until recently, the gas was sold via the Swiss trader RosUkrEnergo, in which Russian energy giant Gazprom holds a 50% stake.
RosUkrEnergo was established in July 2004 on a parity basis between Gazprom and Naftogaz as the exclusive supplier of natural gas to Ukraine.
Naftogaz Deputy Board Chairman Volodymyr Trikolych said last week the company's debt to RosUkrEnergo stood at around $1.3 billion and that Naftogaz had no debt to Gazprom.
Russian President Dmitry Medvedev ordered Gazprom last week to recover Ukraine's debt, stressing the importance of receiving full payment for gas supplies given financial pressure on Russia due to the credit crunch and falling oil prices.
