Obama, who is making his first official visit to Moscow, also referred to US plans for a missile-defence system in Europe, which Russia has opposed.
"I have made it clear that this system is directed at preventing a potential attack from Iran, and has nothing to do with Russia," he said.
"I want us to work together on a missile defence architecture that makes us all safer. But if the threat from Iran's nuclear and ballistic missile programs is eliminated, the driving force for missile defence in Europe will be eliminated. That is in our mutual interest."
Neave Barker, Al Jazeera's correspondent in Moscow, said despite Russian opposition to the defence shield, the two sides have "still been able to move forward in other key areas".
He added that efforts to restore ties between the two nations has been welcomed in Moscow.
"The focus here in Russia ... is that the US has somehow found a new level of respect for Russia and that's certainly going to be championed here as a triumph for Russia," he said.
Obama, who said he wanted to "reset" relations with Russia, also said the two countries are not "destined to be antagonists".
"The pursuit of power is not longer a zero-sum game," he told graduates of the New Economic School in Moscow, adding: "Progress must be shared".
Praise for Putin
His comments came shortly after he exchanged pleasantries with Vladimir Putin, the Russian prime minister, a week after the two men exchanged a terse war of words.
Obama praised Putin's "extraordinary work" as president and now prime minister, and said their talks were an "excellent opportunity to put US-Russian relations on a much stronger basis."
"We may not agree on everything, but we have consultations that will serve the Russian and the American people," he said.
Putin said: "With you, we link our hopes for the furtherance of relations between our two countries".
Their comments came a week after Obama criticised Putin as a man with one foot stuck in the past.
Barker said: "Undoubtedly by meeting Vladimir Putin it's been a chance for Barack Obama and Vladimir Putin to meet each other at face value and judge essentially how each other should be treated.
"One of the key issues for Russia over the past two days is about restoring respect for the nation in the eyes of the United States, so Obama meeting the prime minister was cetainly key to, in Russian eyes at least, this eventually happening."
On Monday, Obama met Medvedev for talks to agree on a new framework for weapons reductions.
The nuclear framework deal commits the two countries to cut the number of nuclear warheads they each hold after the Strategic Arms Reduction Treaty (Start-I) expires in December.
"Within seven years after this treaty comes into force, and in future, the limits for warheads linked to ... [strategic delivery systems should be] within the range of 1,500-1,675 units," the framework agreement read.
Medvedev said the arms deal was "not only vital for the future of our countries, but will also affect the outlook for world developments in many ways".