The meetings are being widely viewed as a test of Mr. Obama's diplomatic skills as he navigates relations with Russia's two top leaders, President Dmitry Medvedev and his mentor, Prime Minister Vladimir Putin.
Obama and Medvedev struck a preliminary deal to reduce their stockpiles of nuclear warheads to as few as 1,500 each, news agencies report.
The document, signed by the two leaders, is meant as a guide for negotiators as the nations work toward a replacement pact for the START arms control agreement that expires in early December. Each country now has about 2,000 warheads.
Agreements negotiated ahead of time addressed some of the summit's top priorities, including a pact to let the United States use Russian territory and air space to move arms into Afghanistan for the forces fighting extremists there, according to news agencies.
"The United States and Russia have more in common than they have differences," President Obama told reporters at the Kremlin during meetings with Medvedev. "If we work hard in these next few days ... we can make extraordinary progress that will benefit the people of both countries."
Medvedev echoed President Obama's forward-looking tone: "We'll have a full-fledged discussion of our relations between our two countries, closing some of the pages of the past and opening some of the pages of the future," the Russian president said, through a translator. "It is my hope that it will be possible to tackle successfully" a range of problems from the economy to security and energy and the environment.
The Russian leader's comments appeared more optimistic than earlier remarks. Over the weekend, Medvedev said he was "moderately optimistic" about the possibility of success at the summit meeting, noting that under former President George W. Bush, relations between the two countries had worsened, according to the New York Times.
The two sides reportedly remain in a stalemate over the U.S. pursuit of a missile-defense system in Europe. President Obama has been reviewing the plan, which was strongly supported by the Bush administration.
Among his planned activities during the Russia trip, Mr. Obama will outline his vision for U.S.-Russian relations at a speech at the New Economic School. It is unclear whether it will be broadcast on the largely government-controlled television outlets in the country.
The summit starts a weeklong trip for Obama that also features G-8 meetings and a visit with the pope in Italy, and a speech in Ghana.
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