The meeting at Sheremetyevo airport with rights groups and lawyers appeared an attempt by Snowden to find a way out of an increasingly difficult situation as he seeks to escape US espionage charges for leaking sensational details of widespread US surveillance activities.
Participants, including representatives of Human Rights Watch and Amnesty International, told reporters after the meeting that Snowden told them he wanted asylum in Russia since he could not fly out of the country without travel documents.
Snowden has been holed up at the airport's transit zone since arriving on a flight from Hong Kong on June 23 before his US passport was revoked.
Human Rights Watch representative Tanya Lokshina told reporters agency that Snowden said "he wants to stay here".
He has applied for asylum in 21 countries. Moscow said last week that Snowden had withdrawn his application for asylum in Russia after learning it was conditional on not harming US interests.
The Kremlin swiftly responded Snowden could stay in the country if he stops revealing confidential US information, reiterating the position set out by President Vladimir Putin.
"Mr. Snowden could hypothetically stay in Russia if he: first, completely stops the activities harming our American partners and US-Russian relations and second, if he asks for this himself," Putin's spokesman Dmitry Peskov said in comments quoted by Russian news agencies.
The powerful speaker of the Russian lower house of parliament, Sergei Naryshkin, told state television that Russia should grant Snowden asylum, describing him as a "defender of human rights".
"He (Snowden) views the Russian president's position with understanding," said Reznik. "He understands that giving him political asylum will be complicated and will strain ties between Russia and the US.
