The White House on Thursday said it was “extremely disappointed” with the Russian government’s decision to grant National Security Agency leaker Edward Snowden temporary asylum, saying the development damaged an already-strained relationship between the two countries.

“Mr. Snowden is not a whistleblower. He is accused of leaking classified information,” White House Press Secretary Jay Carney said. “He should be returned to the United States as soon as possible.”

Snowden on Thursday left the Moscow airport where he has been staying for more than a month, traveling to an undisclosed location in Russia. He was granted temporary asylum in Russia that allows him to stay there for up to a year.

In response, the White House floated the possibility of Obama skipping a scheduled meeting with Russian President Vladimir Putin in September.

“We are evaluating the utility of a summit,” Carney said of the meeting in Moscow.

Snowden, who leaked extensive details about U.S. phone and Internet surveillance programs, has become a major thorn in the side of the Obama administration. His disclosures have ramped up the debate in Washington about the tradeoffs between national security and privacy — Obama on Thursday will host a bipartisan group of lawmakers at the White House to discuss oversight of the surveillance programs.

Many lawmakers, however, echoed the White House’s reaction to the latest wrinkle in the Snowden affair.

"Russia has stabbed us in the back, and each day that Mr. Snowden is allowed to roam free is another twist of the knife,” said Sen. Chuck Schumer, D-N.Y. “Mr. Snowden is a coward who has chosen to run. Given Russia’s decision today, the President should recommend moving the G-20 summit.

The White House said Obama would still attend the G-20 summit in St. Petersburg in September but remain noncommittal about a scheduled one-on-one meeting between Obama and Putin in Moscow.

But some called for a more significant rebuttal from the White House.

"Americans in Washington should consider this a game changer in our relationship with Russia,” Sen. Lindsey Graham, R-S.C., said. “Today’s action by the Russian government could not be more provocative and is a sign of Vladimir Putin’s clear lack of respect for President Obama.

Added Sen. John McCain, R-Ariz., “It is a slap in the face of all Americans. Today’s action by Putin’s Russia should finally strip away the illusions that many Americans have had about Russia the past few years.”

The White House refused Thursday to outline any possible response to the Snowden developments. Administration officials, despite persistent lobbying, were unable to convince Putin to give into their demands.

And the Snowden episode remains a major public-relations problem for the White House. Though Carney said Snowden was not a whistleblower, 55 percent of those polled in a Quinnipiac Univeristy survey released Thursday said the former government contractor fit that description, while 34 percent called him a traitor.

Snowden, who had been holed up in Moscow’s Sheremetyevo International Airport since June 23, trumpeted his release as just.

“Over the past eight weeks we have seen the Obama administration show no respect for international or domestic law, but in the end the law is winning,” Snowden said in a statement released by WikiLeaks, the anti-government-secrecy group aiding his travels. “I thank the Russian Federation for granting me asylum in accordance with its laws and international obligations.”

Snowden faces a trio of espionage charges back on American soil. As part of his temporary asylum in Russia, Snowden agreed to stop leaking secrets about American surveillance programs — a demand made by Putin.

The U.S. government was not given advance notice of Snowden’s release from the airport, Carney said.

Snowden has also received offers of asylum in Venezuela, Nicaragua and Bolivia but expressed doubts about being able to reach them before he is detained by U.S. officials.