Duma member Vyacheslav Nikonov told reporters of Snowden's intentions after the meeting behind closed doors in the transit zone of Moscow's Sheremetyevo airport.
A photo attributed to a Human Rights Watch representative who attended the meeting was posted on the Guardian and other websites, in the first image to appear of Snowden since the newspaper broke the story of widespread U.S. Internet surveillance based on his leaks.
Snowden is believed to have been stuck in the transit zone since June 23, when he arrived on a flight from Hong Kong, where he had gone before his revelations were made public.
He had been expected to transfer in Moscow to a Cuba-bound flight, but did not get on the plane and had not been seen in public since then.
Snowden earlier made an initial bid for Russian asylum, but President Vladimir Putin said he would have to agree to stop leaking secrets about U.S. intelligence before asylum would be considered. Snowden then withdrew his bid.
Venezuela, Bolivia and Nicaragua recently have offered him asylum, but it is unclear if he could fly to any of those countries from Moscow without passing through airspace of the United States or its allies.
Dmitry Peskov, the spokesman for Putin, told Russian news agencies after the announcement Friday that Russia has not received a new bid for asylum from Snowden and that Putin would continue to insist that Snowden stop leaking information
The activists at the meeting included Sergei Nikitin, head of Amnesty International's Russia office, and Tatiana Lokshina, deputy head of the Russian office of Human Rights Watch. Also taken into the meeting room were Russia's presidential human rights ombudsman Vladimir Lukin, prominent attorney Genri Reznik, and Nikonov.
They came after an email in Snowden's name was sent on Thursday. On Facebook, Lokshina posted the text of the email, which says in part that Snowden wants to make "a brief statement and discussion regarding the next steps forward in my situation."
Hundreds of journalists flocked to the airport, but were kept in a hallway outside the meeting area which was behind a gray door marked "staff only." It was not clear if Snowden would have to come out that door or if he could exit by another route.
The text of the invitation did not directly address the offers of asylum, though it expressed gratitude for asylum offers and says "I hope to travel to each of them." It accuses the United States of "an unlawful campaign ... to deny my right to seek and enjoy this asylum."
Reznik said before the meeting that he expected Snowden called for it in order to seek asylum in Russia.
How much the human rights organizations could influence a Russian asylum bid or other aspects of Snowden's dilemma is unclear. Putin takes a dim view of non-governmental organizations' involvement in political matters.
But an appeal by Snowden to internationally respected groups could boost his status and give Russia a pretext for reconsidering asylum.
Russia has said it cannot extradite him because by remaining in the transit zone he is technically outside Russian territory.
Jim Heintz in Moscow contributed to this report.
Copyright 2013 The Associated Press.