Russian President Dmitry Medvedev and U.S. President-elect Barack Obama agreed to meet soon during a telephone conversation on Saturday, a Kremlin spokesman said.
He said the meeting would most probably take place when they were in Washington for the Group of 20 summit next weekend, Reuters reported.
The G20, comprising major industrialized powers and leading developing countries, will meet to discuss how to tackle the global financial crisis.
The Kremlin spokesman declined to give details of the call, saying only that Medvedev congratulated Obama on his successful campaign for the presidency.
Washington's relations with Moscow plunged to a post-Cold War low during George W. Bush's presidency, and many in Russia have been cautiously hopeful for an improvement under Obama.
But hours after Obama won the U.S. presidential election, Russian President Dmitry Medvedev accused Washington of "conceit" in causing turmoil on world markets and said it partly triggered Moscow's war with Georgia in August.
Poland said earlier on Saturday that Obama had declared he would continue with the missile shield, but an Obama aide in Washington said he had given no commitment to deploy the system.