In his most extensive remarks on human rights and democracy on this overseas trip, President Obama said that nations and governments that promote the rule of law and respect the will of its citizens succeed while those who do not, fail.
"The arc of history shows us that governments which serve their own people survive and thrive. Governments which serve only their own power do not. Governments that represent the will of their people are far less likely to descend into failed states, to terrorize their citizens, or to wage war on others," Obama said in a speech at the commencement ceremony for the New Economic School, a Russian graduate program in economics.
Obama applauded Russian President Dmitry Medvedev for his call for judicial reform here, saying, "People everywhere should have the right to do business or get an education without paying a bribe. That is not an American idea or a Russian idea. That's how people and countries will succeed in the 21st century."
"By no means is America perfect. But it is our commitment to certain universal values which allows us to correct our imperfections, and to grow stronger over time," the president said. "If our democracy did not advance those rights, I -- as a person of African ancestry -- wouldn't be able to address you as an American citizen, much less a president."
Obama stressed that the United States does not want to impose its own system of values or government on another nation, noting that his administration supports restoring Honduran President Manuel Zelaya to power even though he has strongly opposed American policies.
"We do so not because we agree with him. We do so because we respect the universal principle that people should choose their own leaders, whether they are leaders we agree with or not," he said.
Zelaya met today with Secretary of State Hillary Clinton, who said following the meeting that Costa Rican president Oscar Arias has agreed to mediate the political and constitutional crisis in Honduras.
However, her remarks did not go as far as those of the president's in Russia. Clinton would only say that the United States would not like to see Zelaya attempt a return to Honduras as he did on Sunday, sparking violent protests in the capital. Instead, she expressed hope that a dialogue process "can begin as soon as possible."
Russian opposition leaders responded positively to Obama's speech, but they pointed out that Obama's summit was mainly talk and that no concrete plans had been made.
"For the first move, for sort of an opening, I think it was very impressive," said former chess champion and presidential candidate Garry Kasparov. "Take it for face value, I still think it's a step forward from what we saw in the previous administration."
Boris Nemtsov, deputy prime minister under former Russian President Boris Yeltsin and a strong critic of the current government, said U.S.-Russia relations still have a long way to go.
"The idea [of resetting relations] was very bright but I think it will be very hard to put it into effect because there is no trust between our countries," Nemstov said.
Obama: U.S., Russia Are No Longer Antagonists
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.
Moving Beyond 'Grayish Moods' that Marked U.S.-Russia Relations
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?"
Obama avoided the pointed question, while standing next to Medvedev, and instead noted Medvedev's and Putin's titles, adding that Russia allocates power in its own way.
"[M]y interest is in dealing directly with my counterpart, the president, but also to reach out to Prime Minister Putin and all other influential sectors, in Russian Society, so that I can get a full picture of the needs of the Russian people and the concerns of the Russian people," he said.
Later today Obama meet again with Medvedev and attend a summit of business leaders with the Russian president. Obama will meet with representatives of Russian civil society organizations and Russian opposition leaders in separate meetings after that.
ABC News' Alex Marquardt, Ann Compton and Kirit Radia contributed to this report.