"I think it is in America's interest and the world's interest that we have a constructive relationship with Russia. That's been my approach throughout my presidency. Where our interests have overlapped, we've worked together," Obama told reporters at his final press conference at the White House, before handing power to Donald Trump.
He, however, admitted that bilateral ties reverted to an "adversarial spirit" when Putin began his second stint as Russian president in 2012.
Obama made clear that the US imposed sanctions on Russia not because of nuclear weapons issues.
"It was because the independence and sovereignty of a country, Ukraine, had been encroached upon, by force, by Russia.That wasn't our judgement; that was the judgement of the entire international community," he said.
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Trump has vowed to have better relations with Russia and in an interview recently said he would propose offering to end sanctions on Moscow in return for a nuclear arms reduction deal.
Obama's administration imposed the sanctions in 2014 after Russia's annexation of the Crimea peninsula from Ukraine.
"It is important for the US to stand up for the basic principal that big countries don't go around and invade and bully smaller countries," he added.
Obama said he worked on a nuclear arms control agreement with Moscow early in his presidency, resulting in the Strategic Arms Reduction Treaty.
"I was prepared to go further.I told President Putin I was prepared to go further.They have been unwilling to negotiate," Obama said.
"If President-elect Trump is able to restart those talks in a serious way, I think there remains a lot of room for our two countries to reduce our stockpiles.And part of the reason we've been successful on our nonproliferation agenda and on our nuclear security agenda is because we were leading by example.I hope that continues," he said.
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