Fugitive US intelligence leaker Edward Snowden on Thursday left the Moscow airport where he has been holed up for over a month, after being granted one year's asylum in Russia, his lawyer said.

Russia's shock decision to award Snowden asylum just two weeks after the application was made risks a diplomatic row with the United States, which had previously described such a prospect as "deeply disappointing".

"Snowden has left Sheremetyevo airport. He has just been given a certificate that he has been awarded temporary asylum in Russia for one year," his lawyer Anatoly Kucherena told AFP.

An airport spokeswoman for Sheremetyevo confirmed he had left within the last two hours. A source told the Interfax news agency he had now crossed the Russian border for the first time.

Kucherena said Snowden had left in a normal taxi on his own, in an apparent cloak-and-dagger operation that went unnoticed by the media who have tried to follow his every move for weeks.

The lawyer, who had held several meetings with Snowden and helped him make his asylum application on July 16, added his new place of residence would be kept secret for security reasons.

"His location is not being made public for security reasons since he is the most pursued man on the planet. He himself will decide where he will go," Kucherena said.

Snowden, 30, is wanted on felony charges by the United States after leaking details of vast US surveillance programmes, but Russia has refused to extradite him.

Interviewed by Rossiya 24 television, Kucherena held up a scanned copy of Snowden's certificate granting him a year's temporary asylum in Russia.

"He has gone to a safe place. I hope you will be understanding about this information," he told the television.

"He may stay in a flat or in a hotel so since he is the most pursued man on Earth he today will be working on security questions."

The name "Snowden Edward Joseph" appears in the asylum document shown on television next to the black and white photo of the bespectacled fugitive.

It was issued on July 31, valid until July 31 of 2014, and is complete with his fingerprint.

Kucherna said that Snowden would eventually emerge into public view and give interviews to the press. But he said Snowden first required an "adaptation course" after so long in the transit zone.

Snowden has been staying in the transit zone of the Sheremetyevo airport north of Moscow since he flew in from Hong Kong on June 23. Until now, he had never formally crossed the Russian border.

His awarding of asylum status in Russia came two days after US soldier Bradley Manning was convicted of espionage on Tuesday for leaking US secrets to anti-secrecy website WikiLeaks.

"Edward Snowden has successfully acquired refugee status in Russia and will shortly leave the airport," WikiLeaks, which has supported Snowden, said on Twitter.

It said he was still "under the care" of WikiLeaks British staffer Sarah Harrison who flew in with him from Hong Kong and is believed to have been with him ever since.

President Vladimir Putin's foreign policy advisor Yury Ushakov rapidly sought to limit the potential diplomatic damage, saying that the situation should not affect relations with Washington.

He also played down speculation that the dispute over Snowden could prompt President Barack Obama to cancel a planned visit for bilateral talks to Moscow in September ahead of the Saint Petersburg G20 summit.

"This situation is rather insignificant and should not influence political relations between Russia and the US," Ushakov said.

"We know what sort of noise surrounds this (situation) in America, but we have not received any signals from the United States" regarding the cancellation of Obama's visit to Moscow, he added.

Putin's Kremlin had sought to distance itself from the whole affair, saying the question was in the hands of the migration authorities.

However there was no indication until now that an asylum application -- that can take up to three months can process -- would be handled so fast.