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 generated by the Der Spiegel report, 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.
A spokesman for Herman Van Rompuy, the president of the European Council, said, "The European Union has demanded and expects full and urgent clarification by the U.S. regarding the allegations."
According to Der Spiegel's report, which it said was partly based on information leaked by Snowden, NSA planted bugs in the EU's diplomatic offices in Washington and infiltrated the building's computer network. Similar measures were taken at the EU's mission to the United Nations in New York, the magazine said.
It also reported that the NSA used secure facilities at NATO headquarters in Brussels to dial into telephone maintenance systems that would have allowed it to intercept senior officials' calls and Internet traffic at a key EU office nearby.
As for Snowden, White House national security spokeswoman Caitlin Hayden said the White House won't comment on specific asylum requests but reiterated its message to all countries that he "needs to be expelled back to the U.S. based on the fact that he doesn't have travel documents and the charges pending against him."
Regarding possible effects on U.S. interactions with Russia, she said it remains the case "that we don't want this issue to negatively impact the bilateral relationship."
Associated Press writers Vladimir Isachenkov in Moscow, Sarah DiLorenzo in Paris, Frank Jordans and Geir Moulson in Berlin, Elena Becatoros in Athens, Raf Casert in Brussels, Deb Riechmann in Brunei, Nicole Winfield in Rome, Julie Pace in Dar es Salaam, Tanzania, and Matthew Lee in Washington contributed to this report.