"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.
In the letter -- posted on the Facebook page of Lokshina, the Russian Human Rights Watch staffer -- the writer praised the "brave countries" that have offered him support, in the face of what he described as "an unlawful campaign by officials in the U.S. Government to deny my right to seek and enjoy this asylum."
In her Facebook post, Lokshina said she received the e-mailed invitation close to 5 p.m. Thursday and acknowledged that she did not know beforehand if it was real.
A large group of Russian and international journalists gathered at the airport in anticipation of the meeting.
Latin American asylum offers
Since his arrival in Moscow, Snowden -- who faces espionage charges in the United States -- has requested asylum in dozens of countries, sparking a surge in speculation about his next steps.
Snowden has admitted releasing classified documents about U.S. surveillance programs to the media and argues that he did so to expose serious violations of the U.S. Constitution.
He is slammed as a traitor by critics and hailed as a hero by his supporters.
WikiLeaks said in a Twitter post Wednesday that Snowden's "flight of liberty" campaign was starting, promising further details.
But details about where Snowden is going -- and how he'll get there -- have remained hard to come by.
U.S. officials told Chinese officials in Washington this week that they're disappointed with the way China and Hong Kong handled the Snowden case, saying their actions undermined trust. China said that Hong Kong authorities acted in accordance with the law.