details of its vast spying operations, is now spending a fourth week in the transit lounge at Moscow's Sheremetyevo airport without crossing the Russian border.
"The application has been filed with the Russian authorities" through the Federal Migration Service (FMS), prominent lawyer Anatoly Kucherena, who has been in contact with Snowden, told AFP.
"I have just left him," he said after meeting the fugitive earlier on Tuesday. Federal Migration Service officials declined to comment immediately.
Kremlin-friendly lawyer Kucherena participated in Snowden's meeting with rights activists and pro-Kremlin lawmakers at Sheremetyevo last week and said Snowden had contacted him for consultations after the get-together.
"He is actively consulting with me," Kucherena said earlier Tuesday. "After the meeting we've been in frequent touch."
Snowden flew into Russia from Hong Kong on June 23 and has since been marooned in the transit zone of Sheremetyevo.
He was checked in for an Aeroflot flight to Cuba on June 24 but never boarded the plane.
On Monday, President Vladimir Putin said Snowden would leave Russia "as soon as he can," likening him to an unwanted gift.
But he accused Washington of "trapping" the American in Moscow, saying no country wanted to take in Snowden due to US pressure.
Kucherena said he was helping Snowden negotiate the complexities of Russian legislation and the difference between the status of refugee, political asylum and temporary asylum.
"Before our consultations he did not have an understanding of those issues," the lawyer said. "He needs to understand what suits him and what rights and obligations a certain status will generate."
Breaking silence for the first time since he arrived, Snowden, who is essentially stateless after Washington revoked his passport, held the closed-door meeting at the airport on Friday.
At the meeting, he said he would file for asylum in Russia before he could work out a way to travel legally to Latin America, asking the activists to petition Putin on his behalf.
Venezuela, Bolivia and Nicaragua have indicated that they would be open to offering the 30-year-old a safe haven.
Activist Svetlana Gannushkina, who has championed the rights of refugees for decades, said Russian authorities generally considered an application for refugee status for up to three months.
After such an application is accepted, an applicant may live and travel locally, she added.
Gannushkina said the procedures to receive temporary asylum or refugee status were pretty straightforward.
A bid for political asylum is considered by the president but is granted very rarely, she said.
Speaking to AFP earlier Tuesday, she said she was surprised he had taken so long to apply for asylum.
"This is the theatre of the absurd," she said.
"Everyone is playing a role in this. I do not know whether he himself is not taking the necessary steps or whether this is all being played out by other people."
Even though the Kremlin has repeatedly said it had nothing to do with Snowden, political observers have said that his meeting with activists at the state-controlled airport would have been impossible without a green light from the Kremlin.
The head of the Amnesty International in Russia, Sergei Nikitin, said after the Friday meeting, he believed plain-clothed representatives of Russian special services had taken part in the get-together.
Washington has reacted sharply to the possibility that Moscow might offer Snowden a safe haven and accused it of providing him with a "propaganda platform."