Addressing an audience including former Soviet leader Mikhail Gorbachev and graduates at a Moscow business school, Obama said Washington wants to work in partnership with a "strong, peaceful and prosperous Russia."
"This belief is rooted in our respect for the Russian people, and a shared history between our nations that goes beyond competition," he said.
On Monday, Obama met with Russian President Dmitry Medvedev and concluded a series of agreements - including one on nuclear arms reduction - as part of an effort to strengthen ties between the former Cold War rivals.
The two-day summit in Moscow was needed to help "reset" a relationship that, according to Obama, "has suffered from a sense of drift" in recent years.
The president reiterated that in his speech Tuesday.
"This must be more than a fresh start between the Kremlin and the White House, though that is important. ... 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."