"We are evaluating the utility of a summit in light of this and other issues," White House spokesman Jay Carney said.
The Moscow summit -- viewed by the administration as an important meeting to find common ground on foreign-policy issues -- is scheduled to be held ahead of a Sept. 5-6 Group of 20 meeting of government heads in St. Petersburg, Russia.
Sen. Chuck Schumer, D-N.Y., said the Obama administration should do more than consider canceling the Putin meeting.
"Now that Snowden has been set free, I don't think the G20 should be meeting in Russia and I think we should not participate if they do," he told reporters.
Obama still plans to attend the G20 summit, Carney said, explaining he had "no changes in our travel plans to announce."
"Russia has stabbed us in the back," Schumer said. "Each day that Mr. Snowden is allowed to roam free is another twist of the knife."
Sen. John McCain, R-Ariz., called the Russian move "a disgrace and a deliberate effort to embarrass the United States."
In a statement he added Washington should intensify advocacy of human rights and civil liberties in Russia, accelerate European missile-defense programs and press for an expansion of NATO, including membership for the Republic of Georgia, a former part of the Soviet Union.
The issue of Georgian membership in NATO has prompted harsh criticism from Russia, as have NATO plans for a missile-defense system.
"Now is the time to fundamentally rethink our relationship with Putin's Russia," McCain said.
Officials told The Wall Street Journal the White House was evaluating more punitive actions, but U.S. options were limited.
The tumult started Thursday after Moscow granted Snowden "temporary refugee" status, giving him asylum in Russia until July 31, 2014.
The asylum, which is typically renewable, lets him live, work and travel in Russia and seek citizenship if he stays in the country for five years.
Snowden thanked Russia for giving him permission to enter the country "in accordance with its laws and international obligations," said a statement from WikiLeaks, which has been helping Snowden since he started disclosing highly classified surveillance efforts to the press in June.
Snowden, 30, could still decide to seek permanent asylum in another country but said last month he wanted to stay in Russia until he could secure safe passage to Latin America.
Venezuela, Bolivia and Nicaragua have offered him asylum. Ecuador has said it would consider granting it to him if he can reach Ecuadorean territory.
Snowden does not have a valid international travel document after the State Department canceled his U.S. passport.
U.S. officials have said they will permit Snowden only to return to the United States, where he faces espionage charges.
Putin, who spent Thursday at his official residence on the outskirts of Moscow, made no immediate public comments about Snowden.
The Kremlin has said for weeks the asylum decision would be made by immigration officials and not by Putin himself, although it is widely assumed the decision would require Kremlin approval.
Putin earlier urged Snowden to go elsewhere and emphasized the U.S. fugitive's arrival was an unwanted surprise to the Kremlin.
Kremlin foreign-policy aide Yuri Ushakov, a former ambassador to the United States, played down the implications of Moscow's Snowden decision Thursday.
"This situation is too insignificant to affect political relations," the Journal quoted him as saying.
Ushakov said Moscow received no indication from Washington the September Obama-Putin summit might be canceled.
He reiterated Putin's expressed hope the incident doesn't hurt U.S.-Russian relations.
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