The White House expressed anger and dismay on Thursday after Russia granted temporary asylum to the American whistleblower Edward Snowden and allowed him to leave the Moscow airport where he had been holed up for over a month.

White House spokesman Jay Carney said the US was "extremely disappointed" by the decision, almost certainly taken personally by President Vladimir Putin. He said Moscow should hand Snowden back and hinted that Barack Obama might now boycott a bilateral meeting with Putin in September, due to be held when the US president travels to Russia for a G20 summit.

Carney added that Snowden had arrived in both China and Russia carrying with him thousands of top secret US documents. He said: "Simply the possession of that kind of highly sensitive classified information outside of secure areas is both a huge risk and a violation.

"As we know he's been in Russia now for many weeks. There is a huge risk associated with … removing that information from secure areas. You shouldn't do it, you can't do it, it's wrong."

With US-Russian relations now at a cold war-style low, Snowden slipped out of Sheremetyevo airport on Thursday afternoon. His lawyer, Anatoly Kucherena, said Russia's federal migration service had granted him temporary asylum for one year. Snowden had left the airport to stay at an undisclosed location with expatriate Americans, he added.

Putin made no immediate comment. But having weighed Russia's options for some weeks, he appears to have decided that Snowden's propaganda value outweighs any possible US repercussions. Obama's already floundering attempts to "reset", or improve, relations with Moscow are in effect over.

In a statement released by WikiLeaks, Snowden thanked the Russian authorities and accused the US of behaving illegally. He made no explicit mention of the trial of Bradley Manning, who this week was convicted of espionage and faces 136 years in jail.

Snowden said: "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."

He added: "I thank the Russian Federation for granting me asylum in accordance with its laws and international obligations."

Snowden has been given a temporary Russian travel document, with his name in Cyrillic and a fresh passport photo. "This gave him the right to temporary asylum on the territory of the Russian Federation, Kucherena said, holding up a copy of the document. US authorities had cancelled his American passport.

Security officials said Snowden officially crossed the border into Russia from the airport's transit zone at about 3.30pm local time. Russia had apparently not informed the US of the move in advance. The state TV channel Rossiya 24 showed a photograph of Snowden's departure, as he clambered into a grey unmarked car.

Despite being pictured from behind Snowden was instantly recognisable wearing his trademark grey shirt and carrying a black backpack. Next to him was Sarah Harrison, the WikiLeaks representative who accompanied him last month on his flight from Hong Kong.

Kucherena declined to provide details on where Snowden was heading, citing safety concerns. "Since he is the most hunted person in the world, he will address the question of security today," he told journalists.

The former NSA employee will himself choose his place of residence and forms of protection, he added. Previously, some speculated that the Russian government was keeping Snowden hidden, although the whistleblower and his lawyer have denied that, adding that he has had no contact with Russian security services.

The whistleblower's father, Lon Snowden, had reportedly been planning to visit his son. Kucherena said on Wednesday that he was sending an invitation to Snowden's father so he could obtain a Russian visa. Kucherena told Rossiya 24 on Thursday that he would be speaking to the father later in the day to arrange his visit.

US authorities have repeatedly called on Moscow to return the fugitive to face charges in America. Last week America's attorney general, Eric Holder, sent a letter to Russia's justice minister promising that Snowden would not be tortured and that he would not face the death penalty if handed over to the US.

Russian officials previously said they had no jurisdiction to return Snowden, as he was not officially located on Russian territory, and that the US had not filed an official extradition request.

The Kremlin did not immediately comment on Snowden's temporary asylum. Putin has previously said repeatedly that to remain in Russia, Snowden must stop activities harming the United States. His lawyer suggested that fresh revelations published by the Guardian on Wednesday and Thursday had come from documents that Snowden had already given the paper before Putin made his comments.

Russia's decision has emboldened hawkish critics of the White House, who have long dubbed Obama's attempts to improve relations with Putin as naive and inappropriate. In a statement on his website, Senator John McCain said: "Russia's action today is a disgrace and a deliberate effort to embarrass the United States. It is a slap in the face of all Americans. Now is the time to fundamentally rethink our relationship with Putin's Russia."

He proposed in response to expand the Magnitsky Act list of banned Russian officials, push for Georgia's acceptance into Nato and implement US missile defence programmes in Europe.

At the White House, Carney made it clear that President Obama was frustrated by the decision by Russia to allow Snowden to enter the country, and that a planned presidential summit was now in jeopardy.

Obama is scheduled to travel to Russia in September for at meeting of G20 leaders in St Petersburg. He also planned to meet Putin for a bilateral summit during the trip in what would have been a sign of improving relations between the two powers.

That meeting is now under review. "Obviously this is not a positive development," Carney said. "We have a wide range of interests with the Russians. We are evaluating the utility of the summit."

Amnesty International called for the focus to switch from Snowden's asylum plight to the "sweeping nature and unlawfulness" of the US government's surveillance programmes.

Widney Brown, senior director for international law and policy at Amnesty, said in a statement: "Now that Edward Snowden has left the airport and has protected status in Russia, the focus really needs to be on the US government's surveillance programs. Snowden would not have needed temporary asylum but for revealing the sweeping nature and unlawfulness of a massive system of domestic and international surveillance by the United States government."

A survey showed that 43% of Russians supported granting Snowden asylum and 51% approved of his whistleblowing activities. Kucherena said he had received numerous letters from Russians offering Snowden lodging, protection and money, as well as from women interested in Snowden romantically.

Pavel Durov, the founder of Russia's most popular social network, VKontakte, invited Snowden to come work as a programmer at the network, in a post on his VKontakte page on Thursday.