"Naturally, with the appearance of a new administration we are counting on the development of relations between our two countries, as a lot of problems have built up in our ties of late," Medvedev said at a meeting with Russian Ambassador to the United States Sergei Kislyak.
Russia-U.S. relations have been frayed by Washington's plans to deploy elements of a missile shield to Central Europe, Russia's five-day war with Georgia over South Ossetia last August, and NATO's eastward expansion.
The Russian president added that there were grounds from optimism judging by recent statements made by "the president-elect and by people who will be in his administration."
At a confirmation hearing before the Senate Foreign Relations Committee on Tuesday, Obama's choice for secretary of state, Hilary Clinton, said she planned to work very closely with Russia on key economic, security, nonproliferation, and arms control issues.
Obama said last month that he wanted to "reset" relations between Washington and an "increasingly assertive" Moscow.
"We want to cooperate with them where we can, and there are a whole host of areas particularly around nonproliferation of weapons and terrorism where we can cooperate, but we also have to send a clear message that they have to act in ways that are not bullying their neighbors," he said.