Describing Russia's decision to grant asylum to Snowden as a "stab in the back", the United States Thursday warned that the move will have serious repercussions on the relationship between the two countries.

As the American whistleblower Edward Snowden moved out of the transit zone of Moscow's airport after getting temporary asylum in Russia, the White House spokesman Jay Carney said "We're extremely disappointed that the Russian government would take this step despite our very clear and lawful requests in public and in private to have Mr Snowden expelled to the United States to face the charges against him."

"We're evaluating the utility of a summit in light of this and other issues," said Jay Carney.

President Obama is scheduled to meet his Russian counterpart Vladimir Putin on the sidelines of the G20 summit this fall in Russia, however, Democrat Senator Chuck Schumer has urged the U.S. president to recommend relocating the summit away from Russia.

While consistently playing down the Snowden issue, the Moscow government said its decision shouldn't affect the relationship between the two countries.

"We are aware of the atmosphere being created in the U.S. over Snowden, but we didn't get any signals [indicating a possible cancellation of the visit] from American authorities," said Yuri Ushakov, an aide to President Putin, according to the RIA Novosti.

Edward Snowden has been granted temporary asylum in Russia until July 31, 2014, and his lawyer said he had left the airport and was headed to an undisclosed but secure location.

The lawyer added that his location is being kept secret because he is the "most wanted person on Earth."

Snowden wants to travel to a country in Latin America for permanent asylum unless he can get assurance of a fair trial by the U.S. government.

However, following Bradley Manning's sentence of 136 years in jail in recent days on charges of espionage, Snowden is very unlikely to go back to the United States to face the two felony charges -espionage and theft of government property.