First meetings between American and Russian leaders are fraught with historical significance. Premier Nikita S. Khrushchev famously pummeled President John F. Kennedy in 1961 during a two-day grilling in Vienna at a meeting Mr. Kennedy characterized as the “roughest thing in my life”; shortly after that meeting, Mr. Khrushchev began building the Berlin Wall.

President George W. Bush and President Vladimir V. Putin established a personal rapport in Slovenia in 2001 that was badly eroded later by a string of contentious issues, like America’s plans to locate a missile defense system in Eastern Europe against Russian wishes.

Mr. Obama walked into the meeting with Mr. Medvedev on Wednesday, his aides said, determined not to repeat past mistakes. After initial pleasantries  the two men discussed their shared interest in law  Mr. Obama, the aides recounted, said, “All right, let’s get down to business,” and began discussions that included Afghanistan, Iran, missile defense and human rights.

Mr. Obama brought up Lev A. Ponomaryov, a Russian human rights leader and frequent Kremlin critic, who was beaten late Tuesday outside his Moscow home. The president did not, however, mention the jailed former tycoon Mikhail B. Khodorkovsky, who is being tried in Russia on charges of tax evasion and other offenses that his supporters claim are trumped up.

A joint statement released after the meeting promised a “fresh start in relations between our two countries,” and White House officials said Mr. Obama would visit Moscow in July.

“We, the leaders of Russia and the United States, are ready to move beyond cold war mentalities,” the two men said in the statement. “In just a few months we have worked hard to establish a new tone in our relations. Now it is time to get down to business and translate our warm words into actual achievements of benefit to Russia, the United States and all those around the world interested in peace and prosperity.”

But clear problems between the nations remained visible, even when viewed through the prism of the joint statement, which sought to emphasize common ground. On European missile defense, for instance, the statement acknowledged “that differences remain” but said that Mr. Obama and Mr. Medvedev looked into possibilities for cooperation, “taking into account joint assessments of missile challenges and threats.”