The NSA whistleblower Edward Snowden has been granted temporary asylum in Russia and has left the Moscow airport where he had stayed for over a month, his lawyer said on Thursday afternoon.

Anatoly Kucherena told journalists at Sheremetyevo airport that Russia's Federal Migration Service had granted Snowden temporary asylum for one year. The lawyer said that he had passed documents confirming this status from the migration service to Snowden, who left the airport for a "safe place".

"This is a certificate that gives him the right to temporary asylum on the territory of the Russian federation," Kucherena said, holding up a copy of the document.

A security official said Snowden had crossed the border into Russia at about 3.30pm local time, and a source at the airport confirmed the American had left, the state news agency RIA Novosti reported.

Snowden has been sought by US authorities since he began leaking documents revealing extensive secret surveillance programmes conducted by the National Security Agency and others. He remained in the airport transit zone for more than a month after the US annulled his American passport while he was flying from Hong Kong on 23 June. Arguing that the US was preventing him from travelling on to South America, where three countries had said they were willing to grant him asylum, Snowden applied for temporary asylum in Russia on 16 July.

According to Kucherena, the whistleblower left the airport alone in an ordinary taxi. The lawyer 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. Although Snowden had originally said he intended to eventually move on to South America, more recently he had indicated that he wants to stay in Russia for the long term. Kucherena previously said Snowden has been reading classic Russian literature and learning the language. In an interview on Thursday with Rossiya 24, a Russian television channel, he said Snowden had no plans to leave Russia for another country.

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 Lon Snowden later that 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.

WikiLeaks announced that Snowden would make a statement on Thursday about the whistleblower Bradley Manning, who was found guilty of espionage on Wednesday.