"If he wants to go somewhere and there are those who would take him, he is welcome to do so," Putin said. "If he wants to stay here, there is one condition: He must stop his activities aimed at inflicting damage on our American partners, no matter how strange it may sound coming from my lips."
Obama said "there have been high-level discussions with the Russians" about Snowden's situation.
"We don't have an extradition treaty with Russia. On the other hand, you know, Mr. Snowden, we understand, has traveled there without a valid passport, without legal papers. And you know we are hopeful that the Russian government makes decisions based on the normal procedures regarding international travel and the normal procedures regarding international travel and the normal interactions that law enforcement has. So I can confirm that."
Putin didn't mention any Snowden effort to seek asylum in Russia, and spokesman Dmitry Peskov declined to say what the Russian response might be. Putin insisted that Snowden wasn't a Russian agent and that Russian security agencies hadn't contacted him.
Three U.S. officials, speaking on condition of anonymity because they weren't authorized to publicly discuss the Snowden case, said Washington's efforts were focused primarily on persuading Russia to deport Snowden either directly to the United States or to a third country, possibly in eastern Europe, that would then hand him over to U.S. authorities.
In a sign of the distrust the latest report had revealed, the German government said it had launched a review of its secure government communications network and the EU's executive, the European Commission, ordered "a comprehensive ad hoc security sweep."
U.S. Secretary of State John Kerry said Monday he didn't know the details of the allegations, but he still played them down, maintaining that many nations undertake various activities to protect their national interests. Kerry failed to quell the outrage from allies, including France, Germany and Italy.