But once Mr. Snowden was ensconced in the airport, the prospect of his long-term presence in Russia apparently seemed less appealing. His first request for asylum two weeks ago was discouraged, and Russia has taken pains to portray itself as neutral. Since then, Mr. Snowden’s options have narrowed, and so have the Kremlin’s, said Dmitri V. Trenin, the director of the Carnegie Moscow Center, a research center in Moscow.

“They cannot keep him here indefinitely, they cannot extradite himself to the U.S., they cannot send him out of the country so that he can be picked up,” Mr. Trenin said. “The government at this stage feels they have to do something to end this stalemate, and the only way to end the stalemate is to go to a default position — that has always been that he stays in Russia and observes certain rules.”

The Kremlin has laid some groundwork for holding Mr. Snowden on a more permanent basis. Ten days ago, perhaps in an attempt to limit damage to the bilateral relationship, Mr. Putin said Mr. Snowden could stay only if he agreed to “cease his work aimed at inflicting damage on our American partners.” A number of conservative, Kremlin-connected figures have praised Mr. Snowden as a defender of human rights and called for granting asylum.

On Friday evening, President Obama talked to Mr. Putin by phone in their first conversation since Mr. Snowden arrived in Moscow. The White House offered no details about the call, other than to issue a statement saying the two had discussed “the status of Mr. Edward Snowden” as well as issues like counterterrorism and the 2014 Winter Olympics in Sochi, Russia.

Earlier Friday, Mr. Putin’s spokesman reiterated the Russian president’s previous offer, and human rights figures who participated in the airport event reported that Mr. Snowden said he accepted the conditions. But Mr. Snowden has said on numerous occasions that he did not think his disclosures had hurt American interests, and it remained unclear whether he planned to continue leaking classified documents.