The American whistleblower Edward Snowden has accused the US of waging a campaign of "historically disproportionate aggression" against him during an extraordinary meeting with human rights activists and Russian officials at the Moscow airport where he has been trapped since 23 June.

In his first appearance since disclosing his identity in the Guardian last month, Snowden insisted he had no regrets and had made a "moral decision" to leak dozens of secret documents outlining US surveillance programmes. He also announced that he would apply for political asylum from the Kremlin and appealed to those present for help in leaving the airport.

The US has lobbied governments around the world to refuse entry to Snowden and has invalidated his US passport.

Last week, a plane carrying the Bolivian president, Evo Morales, was grounded in Vienna after several European countries blocked their airspace amid suspicions that Snowden was on board.

"The government and intelligence services of the United States of America have attempted to make an example of me, a warning to all others who might speak out as I have," Snowden said. "I have been made stateless and hounded for my act of political expression."

White House spokesman Jay Carney has accused Russia of "providing a propaganda platform" for Snowden, which "runs counter to the Russian government's previous declarations of Russia's neutrality".

He said during a White House briefing: "It's also incompatible with Russian assurances that they do not want Mr Snowden to further damage US interests." He urged Russia to hand Snowden over to face charges in the US but added that the US didn't want the affair to damage America's relations with Russia. Pointedly, he said the Russian government should permit human rights groups to do their work "throughout Russia, not just at the Moscow transit lounge".

The US president, Barack Obama, spoke to his Russian counterpart, Vladimir Putin, by telephone on Friday evening but there was no breakthrough on the issue.

Carney said: "We continue to discuss with Russia our strongly held view that there is absolute legal justification for him to be expelled, for him to be returned to the United States, to face the charges that have been brought against him for the unauthorised leaking of classified information."

Asked about the involvement of Amnesty International and Human Rights Watch, both of which sent representatives to meet Snowden, Carney replied: "Those groups do important work. But Snowden is not a human rights activist or a dissident. He is accused of leaking classified information, has been charged with three felony counts, and should be returned to the United States, where he will be afforded full due process."

Snowden appeared relaxed and in good spirits in camera-phone footage posted on the website of the Russian tabloid newspaper LifeNews. At one point, as he was assailing the US for attempting to "legitimise an illegal affair", an airport announcement broke in. He smiled: "I've heard this many times."

Snowden said he would request asylum in Russia until he was permitted to travel to Latin America. Venezuela has offered him political asylum but he remains unable to travel there without travel documents.

Snowden praised Venezuela, as well as Russia, Bolivia, Nicaragua and Ecuador for "being the first to stand against human rights violations carried out by the powerful rather than the powerless" and for "refusing to compromise their principles in the face of intimidation".

Russia has one of the world's poorest reputations for human rights. In the past week alone, it brought in two big decisions against its main whistleblowers: the lawyer Sergei Magnitsky was found posthumously guilty of committing tax fraud, and a judge announced he would soon issue a verdict against corruption activist Alexei Navalny.

Several officials close to the Kremlin attended Friday's 5pm meeting at Sheremetyevo, including Vyacheslav Nikonov, an MP with Putin's United Russia party, and Vladimir Lukin, Putin's human rights ombudsman. Nikonov said he had asked Snowden how he was enjoying his time in Russia. "He laughed – and said, it's safe here," Nikonov said.

Earlier this month, Snowden withdrew a request for asylum in Russia, a move the Kremlin explained by saying he had not agreed with terms set out by Putin calling on him to "stop bringing harm to our American partners". According to attendees, Snowden argued that his leaks were serving, rather than harming, the American people. "He said he doesn't want to bring harm to the United States and sees himself as a law-abiding citizen and a patriot," Nikonov said.

Sergei Naryshkin, speaker of the Duma and a close Putin ally, said Russia should grant Snowden asylum.

Nikonov and other attendees, including Tanya Lokshina of Human Rights Watch and Sergei Nikitin of Amnesty International, were swarmed by journalists as they arrived at Sheremetyevo. Correspondents mobbed the activists as they made their way toward an airport employee with a sign reading "G9", identified in Snowden's invitation email as the marker that would lead them to him.

Lokshina said the US embassy had contacted her en route to the airport urging her to tell Snowden that the US position was that "he is not a human rights defender, he is not a whistleblower, and that he violated the law and should be held responsible". She said she told Snowden, who responded that "he understands that the US authorities look at the situation in that way, but he completely disagrees with that approach".

The horde followed the airport employee upstairs, with journalists running up downward escalators to get ahead, and the invitees were ushered through a service door guarded by police and into a hallway with a metal detector. Lokshina later said that they did not undergo any security checks and were only asked to not film the event.

The atmosphere was tense as journalists crowded to get footage and quotes after they emerged from the 45-minute meeting. At least one fistfight erupted between two cameramen who punched each other in the ribs.

Friday's proceedings left little doubt that the Russian authorities are actively involved in Snowden's stay at Sheremetyevo. Airport staff organised and conducted the event, and order was kept by a small cadre of police officers. Attendees said the meeting was watched by men in suits, whom Nikitin said looked like government operatives: "I'm no expert, but if a man in a tie is standing there with a military bearing and a serviceman's expression, who is he, a school teacher?"

Nikonov, the Kremlin-friendly MP, agreed: "I think that he [Snowden] has guards, given the circumstances."

Russia has denied any involvement in Snowden's plight and continues to insist he is not on Russian territory since he has not crossed the border at Sheremetyevo. Snowden stressed in his statement that he "did not partner with any foreign government to guarantee my safety. Instead, I took what I knew to the public, so what affects all of us can be discussed by all of us in the light of day, and I asked the world for justice."

Attendees said Snowden looked mentally and physically healthy, despite weeks in the halls of Sheremetyevo. "He smiled, he looked confident, he looked like he believes he's in the right," Nikonov said. "I can't say he impressed me as a well-fed young man, but he's never been very bulky. And he has a great haircut.

"He didn't joke, because he understands the seriousness of the situation."

Nikitin said: "He didn't look scared, he looked cheerful … although his face looked a little pale, you can understand why if a person is located the whole time within four walls."

Some attendees said Snowden appeared desperate to get out of the airport. "I got the feeling that after all this, he just wants to physically get out of these premises, and this is the only way to get out of them," Nikitin said.