Edward Snowden reportedly is seeking asylum in Russia, as the NSA leaker faces diminishing options for getting out of the Moscow airport where he is believed to be staying.

The Interfax news agency cited Kim Shevchenko, the duty officer at the Russian Foreign Ministry's consular office in Moscow's Sheremetyevo airport, as saying that Snowden's representative, Sarah Harrison, handed over his request for political asylum on Sunday.

The confirmation, though, comes after Russia's President Vladimir Putin publicly issued a condition for any asylum request from Snowden -- he must stop leaking America's secrets.

Putin also reportedly said that his government had no plans to hand Snowden over to the U.S. But he said that if Snowden wants to stay in Russia, he must stop leaking documents, a condition Snowden so far has shown no interest in meeting.

Putin addressed the controversy as President Obama, during a visit to Tanzania, reiterated that he's "hopeful" Russia will take up the United States' request for extradition.

"There have been high-level discussions with the Russians about trying to find a solution to the problem," Obama said.

Officials still believe Snowden is in the transit zone somewhere in the Moscow airport. He found his status even more in limbo late last week, as Ecuador revoked travel documents that WikiLeaks, which is aiding Snowden, got from a lower-level Ecuadorian official. Snowden originally was trying to seek asylum in Ecuador.

With the U.S. also revoking Snowden's passport, Snowden has no apparent way -- at the moment -- to leave the Moscow airport without risking arrest.

State Department spokesman Patrick Ventrell, while saying he could not confirm Snowden's latest asylum request, reiterated that the U.S. can issue Snowden "one-entry travel documents" back to the United States, where he would presumably face the charges against him.

Putin said that Snowden considers himself a rights activist, a "new dissident" and compared him to Nobel Peace Prize winner Andrei Sakharov.

Putin wouldn't say if any of the leaders of gas exporting nations attending a summit in Moscow could offer Snowden shelter.

The Associated Press contributed to this report.