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But American officials said they are not negotiating away the European missile defense site. Instead, they hope to convince Mr. Medvedev that the site cannot possibly be used against Russia.

Another area of disagreement is over the former Soviet republic of Georgia, which fought a brief war with Russia last year.

Michael McFaul, director of Russian affairs at the National Security Council, said Mr. Obama made clear the United States would never recognize the regions of Abkhazia and South Ossetia, both breakaways that Russia has recognized as independent states.

But Mr. McFaul said as part of his new strategy of trying to get past differences and focus on areas of agreement, Mr. Obama told Mr. Medvedev all sides can agree another flare-up of violence in the Caucuses is ill-advised.

Ariel Cohen, senior research fellow at the Heritage Foundation, said Mr. Obama’s talks in Moscow “left intact fundamental disagreements between the two countries, including the rights of post-Soviet states to sovereignty and territorial integrity.”

“This includes Georgias and Ukraines territorial integrity and sovereignty. Russia and the U.S. haven’t resolved the most thorny issues: missile defense and Iran,” he said. “Russia has no interest in working on Iran with Obama, nor will it recognize that the U.S. missile defense is no threat to Moscow.”

But former Sen. Sam Nunn, co-chairman of the Nuclear Threat Initiative, which works to reduce the danger of weapons of mass destruction, said the summit represented a critical re-engagement on arms control, and said the military-to-military cooperation the two leaders agreed to will help.

“This channel is critical for identifying new ways to increase launch warning and decision time, develop cooperative early warning and missile defense systems and reduce the role of nuclear weapons in our national security strategies,” Mr. Nunn said.

Mr. Obama on Tuesday visits with Mr. Putin, holds another meeting with Mr. Medvedev, speaks to summits of business leaders and civil society activists, and delivers a commencement speech at the New Economic School. In that speech, Mr. Obama is expected to lay out his challenge to Russia to stop seeing U.S. relations as zero-sum and start looking for areas where they can cooperate.

In the run-up to their meeting, Mr. Obama gingerly stepped into touchy Russian politics, telling a Russian reformist newspaper that new charges against two Russian businessmen were “odd.” Still, he said, he supports Mr. Medvedev’s efforts to fight corruption.

Mikhail Khodokrovsky and Platon Lebedev, two Russian businessmen already serving sentences for tax evasion convictions, face fresh charges.

“Without knowing the details, it does seem odd to me that these new charges, which appear to be a repackaging of the old charges, should be surfacing now, years after these two individuals have been in prison and as they become eligible for parole,” Mr. Obama told Novaya Gazeta, a Russian newspaper whose columnist Anna Politkovskaya, a frequent government critic, was fatally shot in 2006.

In an interview with the newspaper Mr. Obama demurred when asked whether the Russian authorities should be pressured to apprehend her killer.

After the two presidents’ meeting Monday, Mr. McFaul said Mr. Obama did not specifically raise Khodokrovsky in his talks with Mr. Medvedev but said it was “clear” whom the American leader was talking about when he pushed Mr. Medvedev to create a stable business environment.