The New Economic School is a graduate school of economics in Moscow that was established in 1992 as a partnership between Russian economists and Western academics.
He said that the old assumptions that the United States and Russia must be antagonists or "forge competing blocs to balance one another" are no longer tenable.
"In 2009, a great power does not show strength by dominating or demonizing other countries. The days when empires could treat sovereign states as pieces on a chess board are over," he said. "The pursuit of power is no longer a zero-sum game. Progress must be shared."
Obama said that the reset is not just between the Kremlin and the White House, but also between the citizens of both nations.
"It must be a sustained effort among the American and Russian people to identify mutual interests, and to expand dialogue and cooperation that can pave the way to progress," he said, noting the challenge of repairing a strained relationship "between former adversaries, and to change habits that have been ingrained in our governments for decades."
Obama outlined a series of key areas where the United States and Russia can work together to further each country's own national interests: stopping the spread of nuclear weapons and their use; defeating extremists worldwide; and fixing the global economy.
Obama touted the progress he and Medvedev made in their sessions yesterday on the issue of nuclear arms control and expressed his gratitude for the Russian leader agreeing to allow American forces and supplies to fly over Russian airspace en route to Afghanistan.
Obama met Russian Prime Minister Vladimir Putin this morning at his dacha in Moscow, Novo Ogaryovo, for a working breakfast that marked the first time the two leaders had met.
Obama described the session as an "excellent opportunity to put U.S.-Russian relations on a much stronger footing."
"We may not end up agreeing on everything, but I think we can have a tone of mutual respect that will be beneficial to the Russian and American people," Obama said.
Noting that the history of U.S.-Russian relations has "periods our relations flourished and periods of grayish moods," Putin said that with Obama, Russia will "link all our hopes for the further relations of our two countries."
Obama paid compliments to the former president for his work in that position and his work as prime minister.
Putin took Obama over to the windows and pulled back curtains to show the sunny terrace where the two would have breakfast, prompting Obama to joke, "I also want to thank the prime minister for arranging very nice weather." Obama arrived yesterday in Moscow to gray skies but it later cleared up and the sun even came out.
The Putin/Obama meeting comes at a time when Russia analysts say that in fact it is Putin, and not Medvedev, who holds the most power in Russia.
Yesterday, Obama was asked a direct question about whether he has settled in his mind "who is really in charge here in Russia, the president or Prime Minister Putin?"