WASHINGTON (AFP) -- President Barack Obama has confronted Russia over its granting of asylum to fugitive intelligence leaker Edward Snowden and its new anti-gay law, saying Moscow occasionally displays a "Cold War mentality."

During an appearance on a late-night talk show Tuesday, Obama said Moscow was still being helpful in Afghanistan and on counter-terrorism but spoke of "underlying challenges that we've had with Russia lately."

"There have been times where they slip back into Cold War thinking and a Cold War mentality," Obama said on NBC's "The Tonight Show with Jay Leno."

"What I consistently say to them, and what I say to President (Vladimir) Putin, is that's the past, and we've got to think about the future, and there's no reason why we shouldn't be able to cooperate more effectively than we do."

Obama insisted he would attend next month's G20 summit in Saint Petersburg, but did not say whether he would meet with Putin for one-on-one talks in Moscow.

Obama said he was "disappointed" by Russia's decision to award one year's temporary asylum to Snowden, the former IT contractor who leaked details of vast US surveillance programs to the media.

Snowden was last week allowed to relocate to a secret safe house after being marooned in Moscow's airport for five weeks.

Washington had revoked his passport and demanded he be sent back to face charges of espionage over the leaks, which detailed the US National Security Agency's gathering of  vast amounts of phone call logs and Internet data.

Obama declined to say whether the programs had helped identify the Al-Qaeda threat that led Washington to close some two dozen embassies earlier this week, but called them a "critical component of counterterrorism."

Russia's deputy foreign minister Sergei Ryabkov said Tuesday that Washington was blowing the Snowden case out of proportion after the White House said it was still considering whether Obama would meet Putin in Moscow.

"The US administration is bringing into question bilateral contact at the highest level. I think this is absolute distortion of reality, it's looking at the world in a crooked mirror," he said.

Obama also lashed out at Russia over a recent law criminalizing the dissemination of information about homosexuality to minors, which critics fear could legitimize widespread discrimination.

"I have no patience for countries that try to treat gays or lesbians or transgender persons in ways that intimidate them or are harmful to them," Obama said, noting Russia "is not unique" in passing such laws.

The Russian measure, signed into law by Putin, introduces fines of up to 5,000 rubles ($156) for citizens who engage in "gay propaganda," but critics fear it could legitimize homophobia.

The bill has sparked controversy ahead of the 2014 Winter Olympic Games in Sochi and raised concerns that visiting gay athletes and spectators could face discrimination or even legal action.

Obama downplayed such fears, saying it was in the best interests of Putin and Russia to "make sure the Olympics work."

"I think they understand that for most of the countries that participate in the Olympics, we wouldn't tolerate gays and lesbians being treated differently," Obama said.

"They're athletes. They're there to compete. If Russia wants to uphold the Olympic spirit, then every judgment should be made on the track or in the swimming pool or on the balance beams.

"People's sexual orientation shouldn't have anything to do with it."

The White House has said it is assessing the "utility" of the planned summit between Obama and Putin scheduled for early September.

The foreign and defense ministers of the two global powers will meet on Friday in Washington, when they are expected to discuss Syria, Afghanistan and Iran.

Washington and Moscow have been at loggerheads over Syria, with Russia backing President Bashar al-Assad's regime and the United States providing aid to the rebels struggling to topple him.