"Now, we need not to again reset everything ... but to develop ties," Medvedev said in an interview before departing Wednesday to visit Finland.
Following icy ties between the countries when George W. Bush was president, U.S. President Barack Obama made the so-called "reset" of relations a foreign policy priority when he took office four years ago.
Michael McFaul, the U.S. ambassador to Russia, said Obama's second administration would work to build on gains under the "reset policy," including strategic arms reductions and bilateral agreements on visas and adoptions, RIA Novosti reported.
"I can again say that the incumbent U.S. president is a person whom we can deal with, he listens to arguments, can communicate and make decisions," Medvedev said. "I am thankful to him for the years when we worked together. I hope that during his next term, he will stick to the same approaches."
The European missile defense shield remains problematic, Medvedev said. Russia is concerned that the defense shield would harm the country's defense mechanisms, while the United States and European countries said it is meant to protect the continent from rogue nations.
Russia and NATO agreed to cooperate on the missile defense system during the November 2010 summit in Portugal. But NATO wants two independent systems that exchange information while Russia prefers a fully inter-operational joint system.