US intelligence leaker Edward Snowden will stay in the transit zone of the Moscow airport where he has been holed up for three weeks while Russian authorities process his asylum request, a lawyer helping him said Tuesday.

Anatoly Kucherena, a Russian lawyer who helped Snowden file an application for asylum in Russia earlier Tuesday, told AFP the fugitive former National Security Agency (NSA) contractor was happy with his treatment at the airport.

"While all procedural questions are being decided, he will remain in the transit zone of the airport," Kucherena told AFP in central Moscow when asked if Snowden would remain at Sheremetyevo airport until the asylum request was approved.

He confirmed that the asylum procedure could take up to three months, although a shorter period is theoretically possible.

Kucherena said he met Snowden at the airport on Tuesday to file the asylum request, with a translator the only other person present.

"He is satisfied with how he is being treated by the employees of the airport," he added, declining to say how Snowden's security was being ensured at the airport.

Speaking outside his office in a courtyard off a prestigious central Moscow street, Kucherena said he helped Snowden put together the asylum application after the stranded fugitive requested his assistance.

A supporter of President Vladimir Putin who supported Putin's election campaign last year, Kucherena also has a legal practice in Moscow that takes on high-profile cases.

He also sits on the "public council" of the Federal Security Service (FSB), which was created by Putin in 2006.

According to its website, the council works to "develop a relationship" between the security service and the public. Its fifteen members have to be approved by the head of the FSB.

Kucherena was among a group of rights activists, pro-Kremlin lawmakers and lawyers who met Snowden at the airport on Friday, where the fugitive indicated that he wanted to file for asylum in Russia.

Snowden later called Kucherena "by telephone" asking for his help, the lawyer said. He said he did not know why Snowden singled him out.

"I didn't look for him," he said. "Do you have a way of talking with him? I didn't either.

"He reached out to me and asked me to come" after the meeting on Friday, said Kucherena, adding that he had a long meeting with Snowden Monday, when he explained Russian laws.

He then came back to the airport on Tuesday to "put together" the application for the migration service.

The two met in the transit zone, Kucherena said, but said he could not remember which terminal of the airport. At these meetings he said he had not seen Sarah Harrison, the British citizen and WikiLeaks employee who has accompanied Snowden.

"Most likely she has documents," he said, when asked whether Harrison has a Russian visa. "I had no contact with her."

Kucherena said Snowden, who has been marooned in the transit zone since arriving from Hong Kong seeking to escape US justice, has "options".

"Right now he wants to stay in Russia. He has options. He has friends and a lot of supporters.... I think everything will be ok," said Kucherena.

"If his request for asylum status is accepted, he has the same rights as you and me. There is no (other) way to resolve this situation."