"I had a good conversation with him. I hope that with the new administration we will be able to build a normal, full-fledged partnership," Medvedev said in an interview with Le Figaro ahead of his trip to France for a Russia-EU summit due on Friday.
The president said he hoped that "we will find ways out of situations, where with our current colleagues we were unable to."
Asked whether he would meet with Obama in the United States this weekend at a G20 summit of developed and emerging economies on the global financial crisis, Medvedev said it was not clear whether the president-elect would participate.
The timing of the summit, coming at the end of President George W. Bush's presidency, and major disagreements between participants over how to handle the crisis, have led analysts to predict that groundbreaking agreements are unlikely to be reached at the talks.
Medvedev said he and Obama had agreed "to meet without delay... This is important for the United States and the Russian Federation."
Ties between Moscow and Washington have been steadily weakened in recent years over a host of differences, including Iran's nuclear ambitions, American missile defense plans for Central Europe, and most recently Russia's brief war with U.S. ally Georgia in August.
Medvedev last week issued a strong warning to the U.S. over its plans to put interceptor missiles and a tracking radar in Poland and the Czech Republic, and threatened to place short-range Iskander missiles near Poland's border.
Taking a softer tone on Thursday, Medvedev noted that Obama has been elected in a difficult time, but has received "a large credit of trust" from voters.
"I wish him good luck and success in what he has to do," he said.
