Washington (CNN) -- A planned Moscow summit with Russian President Vladimir Putin is being reconsidered because Russia granted asylum to classified leaker Edward Snowden, White House spokesman Jay Carney told reporters on Thursday.
"We are extremely disappointed that the Russian government would take this step despite our very clear and lawful request in public and in private" for Snowden to be returned to the United States to face charges, Carney said.
President Barack Obama is scheduled to visit Moscow for talks with Putin before attending a G-20 gathering in St. Petersburg next month, but Carney said "we are evaluating the utility of a bilateral summit in Moscow."
His remarks made clear that Obama would still attend the G-20 meeting even if he canceled the Moscow stop.
Snowden, who leaked details of classified surveillance programs that sparked a political firestorm in the United States, had been holed up for weeks in the international transit lounge at the Moscow airport.
The administration invalidated Snowden's passport and asked Russia to hand him over, but the granting of asylum for at least a year allowed the former National Security Agency contractor to leave the airport on Thursday.
On Capitol Hill, legislators from both parties backed a strong response by Washington.
Democratic Sen. Chuck Schumer of New York said "Russia has stabbed us in the back, and each day that Mr. Snowden is allowed to roam free is another twist of the knife."
"Given Russia's decision today, the president should recommend moving the G-20 summit" to another country, Schumer said.
The chairman of the House Foreign Affairs Committee, Rep. Ed Royce of California, called Russia's move "absolutely unacceptable" and said Obama "must make clear to President Putin that there can be no 'business as usual' as long as Russia continues to harbor this fugitive from justice."
"He should immediately announce that he will not meet one-on-one with the Russian president at the upcoming G-20 Summit in Russia in September," Royce said. "Putin knows how to play hardball, so should we."
In a joint statement, Republican Sens. Lindsey Graham of South Carolina and John McCain of Arizona labeled Russia's move a "slap in the face of all Americans."
"We cannot allow today's action by Putin to stand without serious repercussions," the senators said, calling for the completion of missile defense programs in Europe that Russia opposes, expanding NATO to include Russian neighbor Georgia and increasing support for those seeking improved human rights in Russia.
Graham had previously suggested a U.S. boycott of the 2014 Winter Olympics in Sochi, Russia, over Moscow's refusal to hand over Snowden. But he quickly backed off under widespread criticism.
Meanwhile, the No. 2 Democrat in the House, Rep. Steny Hoyer of Maryland, noted that relations with Russia were not "on a positive track" before the Snowden case.
"That does not mean we are not talking. It doesn't mean that we don't have very significant mutual interests. We do," Hoyer told reporters. "It doesn't mean that we shouldn't have continuing interface with the Russians because we have a lot of mutual interests that are very important to both countries."
Even before Russia granted Snowden asylum, some in Washington called for Obama to cancel the upcoming trip, or at least the Moscow visit, to demonstrate American disapproval for Russia's failure to immediately turn over the fugitive.
However, Senate Armed Services Committee Chairman Carl Levin of Michigan said Thursday he hoped that Obama would attend the G-20 talks.
A lone "bump" in U.S.-Russia relations should not derail the trip "because there will be a lot of other countries that will be there and a lot of other issues that need to be resolved," Levin told CNN.
Snowden leaked to the media that the NSA had secretly collected and stored millions of phone records from accounts in the United States. The agency also collected information from U.S. companies on the Internet activity of overseas residents, he said.
The revelations sparked a public outcry against what liberals, libertarians and others call excessive government intrusion in the privacy of citizens.
Security officials say the surveillance network was necessary to protect the country against terrorism,and that the programs are under strict judicial and administrative controls.
Supporters of Snowden call him a whistleblower who should not face prosecution, but Carney rejected that characterization Thursday.
"Mr. Snowden is not a whistleblower," Carney said. "He is accused of leaking classified information and has been charged with three felony counts, and he should be returned to the United States as soon as possible, where he will be accorded full due process and protections."
CNN's Gloria Borger, Ted Barrett, Jim Acosta and Virginia Nicolaidis contributed to this report.