But he said that the United States would not accept that the breakaway regions of Georgia were part of Russia's "sphere of influence".
"The United States rejects the notion that NATO's gain is Russia's loss, or that Russia's strength is NATO's weakness," he told a security conference in Moscow.
"The last few years have seen a dangerous drift in relations between Russia and members of our (NATO) Alliance."
He said that Russia and NATO should cooperate to defeat al Qaeda and the Taliban in Afghanistan and work together to pave the way for cuts in their nuclear arsenals.
He added however that the United States would not agree with Russia with everything.
"For example, the United States will not recognise Abkhazia and South Ossetia as independent states. We will not recognise a sphere of influence."
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