Snowden says he won't release harmful US data
Waiting for request
But on Saturday, officials in Moscow said they were still waiting for Snowden's request.
Russian Foreign Minister Sergei Lavrov said Snowden would have to submit his application to the Federal Migration Service, Russian news agencies reported.
The head of Russia's Federal Migration Service, Konstantin Romodanovsky, said Saturday it had received nothing. If it did, he added, the request would be examined according to the usual procedures.
Washington has reacted sharply to the possibility that Moscow might offer Snowden a safe harbor.
"We would urge the Russian government to afford human rights organizations the ability to do their work in Russia throughout Russia, not just at the Moscow transit lounge," White House spokesman Jay Carney said.
"Providing a propaganda platform for Mr Snowden runs counter to the Russian government's previous declarations of Russia's neutrality," he added.
US President Barack Obama spoke to Putin by telephone on Friday on issues including the Snowden affair, the Kremlin and White House both said, but no further details were forthcoming.
Washington has already rebuked China for allowing Snowden to leave for Russia from Hong Kong.
At his meeting with activists, Snowden insisted he did not want to harm the US.
It was not clear, however, if this meant he was prepared to stop leaking intelligence in order to stay in Russia.
Venezuela, Bolivia and Nicaragua have all offered Snowden asylum, but Snowden said Western governments would prevent him from traveling to the region.
A summit of the Latin American Mercosur trade bloc issued a statement Friday reaffirming the right to asylum and rejecting "any attempt at pressure, harassment or criminalization by a state or third parties".
The bloc, meeting in the Uruguayan capital Montevideo, denounced four European countries that denied airspace to a plane carrying Bolivian President Evo Morales back from Moscow earlier this month.