He said Russian and U.S. interests largely overlap in halting the spread of nuclear weapons, confronting violent extremists, ensuring economic prosperity, advancing the rights of people and fostering cooperation without jeopardizing sovereignty.

But he also sprinkled in challenges to Russia, particularly in the area of democracy. U.S. officials are wary of Russia's increasingly hard-line stand on dissent.

"By no means is America perfect," Obama said. But he also said: "Independent media have exposed corruption at all levels of business and government. Competitive elections allow us to change course. ... 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 said the U.S. will not try to impose any kind of governing system on another country. But he argued for democratic values "because they are moral, and also because they work."

On Georgia and Ukraine — two nations that have sought NATO membership to the chagrin of neighboring Russia — Obama tried a diplomatic touch. He defended the steps nations must take to join the alliance, adding, "NATO seeks collaboration with Russia, not confrontation."

The White House described the session positively, on the whole.

Both sides agreed to try to be better listeners and pay more attention to how each side is looking at the same issues, said one senior administration official, speaking on condition of anonymity to discuss details of the private meeting that was described as "very candid."

Before the speech Obama held what the White House characterized as a "good meeting" with former Soviet President Mikhail Gorbachev. The U.S. leader also met with U.S. and Russian business leaders; and was to meet a diverse collection of nongovernment leaders from both countries — health experts, environmentalists, reporters, human rights advocates — who will be holding their own summit to re-engage bilateral cooperation.

Obama also was to meet with Russian opposition leaders.

On Wednesday he heads to a G-8 summit in Italy. While there he will meet Pope Benedict XVI, before moving on to Ghana where he plans to deliver what the White House describes as a major foreign policy speech.