Russian television aired an amateur video of Snowden delivering remarks to the activists.
"A little over one month ago, I had family, a home in paradise, and I lived in great comfort. I also had the capability without any warrant to search for, seize, and read your communications. Anyone's communications at any time. That is the power to change people's fates. It is also a serious violation of the law," he said.
"The immoral cannot be made moral through the use of secret law. I believe in the principle declared at Nuremberg in 1945: Individuals have international duties which transcend the national obligations of obedience. Therefore individual citizens have the duty to violate domestic laws to prevent crimes against peace and humanity from occurring," Snowden said.
Russian asylum conditions?
Snowden's desire to be granted temporary asylum in Russia may represent something of a turnaround.
He last week reportedly withdrew an asylum request with Russian authorities after President Vladimir Putin said he would have to "stop his work aimed at harming our American partners" if he wanted to stay in the country.
"Snowden did voice a request to remain in Russia," Kremlin spokesman Dmitry Peskov said on July 2, according to the Russian news agency RIA Novosti.
"Then, yesterday, hearing President Putin outline Russia's position regarding the conditions under which he could do this, he withdrew his request for permission to stay in Russia."
It's not clear if a request for temporary asylum would entail different conditions.
But a Russian lawmaker who was at Friday's meeting, Vyacheslav Nikonov, told state news agency Itar-Tass that Snowden had said he did not intend to cause any further damage to the United States.
"I've said all I knew and I will not harm the United States in the future," Snowden said, according to Nikonov.
The United States has reached out to the Russians regarding Snowden's meeting with human rights groups, two senior State Department officials told CNN.
Snowden has been technically a free man while in Moscow but has been unable to travel after U.S. authorities revoked his passport when he was charged with espionage.
Sergei Nikitin, head of Amnesty International's Moscow office, who was at the meeting, said he was pleased to voice the organization's support for Snowden in person.
"We will continue to pressure governments to ensure his rights are respected -- this includes the unassailable right to claim asylum wherever he may choose," he said in a statement.
"What he has disclosed is patently in the public interest and as a whistle-blower his actions were justified."
Snowden exposed unlawful sweeping surveillance programs, and states that try to prevent him from revealing such unlawful behavior "are flouting international law," Nikitin said.
"Instead of addressing or even owning up to these blatant breaches, the U.S. government is more intent on persecuting him. Attempts to pressure governments to block his efforts to seek asylum are deplorable," he said.
Jamil Dakwar, human rights program director for the American Civil Liberties Union, said the United States has a long history of supporting asylum rights, but in the case of Snowden, it "has improperly interfered with the right of asylum by revoking his passport and exerting extraordinary pressure on countries to reject his requests.
"Snowden's claims for asylum deserve fair consideration, and U.S. actions to secure his extradition must take place within an acceptable legal framework protecting his right to seek asylum."
U.S. accused of 'unlawful campaign'
The transit zone meeting with Snowden began at around 5 p.m. local time (9 a.m. ET).
A CNN team at the airport saw about half a dozen people -- including Russia's human rights ombudsman and representatives of Amnesty International, Human Rights Watch and Russian human rights groups -- enter a door marked "Private" in Terminal E. Police and security officers then kept the media at a distance.
The letter purportedly e-mailed by Snowden to invite them to the meeting blasted the United States for carrying out illegal actions against him.