The application is for temporary refuge, not permanent political asylum, and Snowden is expected to continue exploring options in Latin America or elsewhere.
"It is a compromise step as Russia doesn't want to utterly spoil its relations with the United States, as tense as they are," said Olga Kostina, head of the rights organization Soprotivleniye. She was among a number of human rights advocates who met with Snowden on Friday at Sheremetyevo International Airport in Moscow, where he has been staying since his arrival from Hong Kong more than three weeks ago.
WikiLeaks, which has been advising Snowden, announced his application in a tweet: "Edward Snowden today has filed for a temporary protection visa with Russia's ministry of immigration."
The Federal Migration Service, which has an office at Sheremetyevo, confirmed that it had received the application. Snowden was reportedly accompanied by Russian attorney Anatoly Kucherena.
"He filled this application in my presence, as there were many legislative and legal questions," Kucherena told the RIA Novosti news agency after meeting with Snowden in the airport's transit zone.
In the application, Snowden said he needs asylum because "he faces persecution by the U.S. government and he fears for his life and safety, fears that he could be subjected to torture and capital punishment," Kucherena said on Rossiya-24 television.
Kostina said that the temporary refugee status could be granted to Snowden within three months, at which point he could leave the airport and move to a center for temporary refugees.
"It is a good way out for Snowden in the given situation, because it could give him more time to decide what to do next," she said. "He told us last Friday that he wanted to travel to one of the countries in Latin America which were ready to grant him political asylum, but considerations of personal security prevailed and he realized that it would be safe for him to stay in Russia even temporarily."
The presidents of Venezuela, Bolivia and Nicaragua have said that Snowden would be welcome in their countries, but his exit from Russia has been complicated by his lack of a valid passport. The United States canceled his passport when it issued a warrant for his arrest.
Russia and the United States do not have an extradition treaty, and President Vladimir Putin has promised that Snowden would not be arrested and sent home for prosecution, although he also has expressed the hope that Snowden would leave Russia soon. Putin also has said that Snowden will not be granted asylum in Russia unless he agrees to stop activities that harm the United States, a condition that Putin said Snowden is unwilling to meet.
Snowden, who worked in Hawaii for the NSA, is wanted on espionage charges for leaking highly sensitive classified data about the agency's surveillance of international Internet and telephone accounts.
The effort to reach a temporary resolution of his situation will allow the Kremlin to formally distance itself, Kostina said. A request for political asylum would have to be decided by Putin, she said.
"If we are talking about temporary shelter, this is not the president's issue," Putin's spokesman, Dmitry Peskov, told reporters Tuesday. "This issue will be decided on the level of the Federal Migration Service."