Moscow (CNN) -- Fugitive American intelligence leaker Edward Snowden is likely to leave the transit zone in Moscow's airport, where he's been holed up for weeks, "in the next few days," his lawyer said Wednesday.
Snowden applied for temporary asylum in Russia on Tuesday from Sheremetyevo International Airport.
He "will leave (the airport) in the next few days because some legal papers are still required to be formalized," Russian attorney Anatoly Kucherena said in Moscow.
"Therefore, I think this issue will be resolved within a week and after this, the question of granting him temporary asylum will be decided upon."
A former National Security Agency contractor, Snowden admittedly leaked documents to the media that exposed sweeping U.S. electronic surveillance programs. He faces espionage charges.
Kucharena, who helped Snowden file his application for asylum, said his client might be able to leave the airport while the request is considered.
Within a few days, Snowden should receive a certificate showing that the asylum request is under consideration, and that certificate will allow him to legally leave the airport's transit area, the attorney said.
It's not clear whether Russia will decide to grant temporary asylum. Snowden has said he wants to stay while awaiting passage to Latin America.
President Vladimir Putin said Monday that Snowden appeared to be "shifting his position somewhat" when it comes to meeting Russia's conditions for asylum, according to state news agency Ria Novosti.
He had earlier said that Snowden would have to "stop his work aimed at harming our American partners" if he wanted to stay.
The Guardian journalist who broke the Snowden story and a spokesman for WikiLeaks have both indicated that Snowden could reveal more secrets.
On Wednesday, Putin told reporters in Moscow that ties between the United States and Russia "are far more important" than any intelligence scandal. The Russian leader said that he believes that Snowden "never intended to stay here, in Russia, forever."
Snowden arrived in Moscow from Hong Kong on June 23. He has been unable to leave because the United States revoked his passport.
The presidents of Venezuela and Bolivia have said their countries would give Snowden asylum, and Nicaragua's president said he would offer it "if circumstances permit."
Snowden appears likely to try to avoid the chance of U.S. capture even if Russia grants him papers to leave.
Washington has no extradition agreement with Russia and FBI agents who work at the American Embassy have no authority to make arrests.
The U.S. government has requested Russia expel Snowden. Absent that, it will watch carefully the route he takes if he tries to reach one of the Latin American countries willing to take him in.
The United States could grab Snowden if any plane carrying him were to refuel in a country that respects U.S. arrest warrants. But he likely will be careful to avoid that scenario.
Nevertheless, the United States has sent provisional arrest warrants to a number of countries where Snowden could either transit or seek asylum, a U.S. official said last week.
CNN's Carol Cratty in Washington contributed to this report.