The US has spied on the staff of prominent human rights organisations, Edward Snowden has told the Council of Europe in Strasbourg, Europe's top human rights body.

Giving evidence via a videolink from Moscow, Snowden said the National Security Agency – for which he worked as a contractor – had deliberately snooped on bodies like Amnesty International and Human Rights Watch.

He told council members: "The NSA has specifically targeted either leaders or staff members in a number of civil and non-governmental organisations … including domestically within the borders of the United States." Snowden did not reveal which groups the NSA had bugged.

The assembly asked Snowden if the US spied on the "highly sensitive and confidential communications" of major rights bodies such as Amnesty and Human Rights Watch, as well as on similar smaller regional and national groups. He replied: "The answer is, without question, yes. Absolutely."

Snowden, meanwhile, dismissed NSA claims that he had swiped as many as 1.7m documents from the agency's servers in an interview with Vanity Fair. He described the number released by investigators as "simply a scare number based on an intentionally crude metric: everything that I ever digitally interacted with in my career."

He added: "Look at the language officials use in sworn testimony about these records: 'could have,' 'may have,' 'potentially.' They're prevaricating. Every single one of those officials knows I don't have 1.7m files, but what are they going to say? What senior official is going to go in front of Congress and say, 'We have no idea what he has, because the NSA's auditing of systems holding hundreds of millions of Americans' data is so negligent that any high-school dropout can walk out the door with it'?"

In live testimony to the Council of Europe, Snowden also gave a forensic account of how the NSA's powerful surveillance programs violate the EU's privacy laws. He said programs such as XKeyscore, revealed by the Guardian last July, use sophisticated data mining techniques to screen "trillions" of private communications.

"This technology represents the most significant new threat to civil liberties in modern times," he declared.

XKeyscore allows analysts to search with no prior authorisation through vast databases containing emails, online chats, and the browsing histories of millions of individuals.

Snowden said on Tuesday that he and other analysts were able to use the tool to select an individual's metadata and content "without judicial approval or prior review".

In practical terms, this meant the agency tracked citizens not involved in any nefarious activities, he stressed. The NSA operated a "de facto policy of guilt by association", he added.

Snowden said the agency, for example, monitored the travel patterns of innocent EU and other citizens not involved in terrorism or any wrongdoing.

The 30-year-old whistleblower – who began his intelligence career working for the CIA in Geneva – said the NSA also routinely monitored the communications of Swiss nationals "across specific routes".

Others who fell under its purview included people who accidentally followed a wrong link, downloaded the wrong file, or "simply visited an internet sex forum". French citizens who logged on to a suspected network were also targeted, he said.

The XKeyscore program amounted to an egregious form of mass surveillance, Snowden suggested, because it hoovered up data from "entire populations". Anyone using non-encrypted communications might be targeted on the basis of their "religious beliefs, sexual or political affiliations, transactions with certain businesses" and even "gun ownership", he claimed.

Snowden said he did not believe the NSA was engaged in "nightmare scenarios", such as the active compilation of a list of homosexuals "to round them up and send them into camps". But he said that the infrastructure allowing this to happen had been built. The NSA, its allies, authoritarian governments and even private organisations could all abuse this technology, he said, adding that mass surveillance was a "global problem". It led to "less liberal and safe societies", he told the council.

At times assembly members struggled to follow Snowden's rapid, sometimes technical delivery. At one point the session's chairperson begged him to slow down, so the translators could catch up.

Snowden also criticised the British spy agency GCHQ. He cited the agency's Optic Nerve program revealed by the Guardian in February. It was, he said, one of many "abusive" examples of state snooping. Under the program GCHQ bulk collects images from Yahoo webcam chats. Many of these images were "intensely private" Snowden said, depicting some form of nudity, and often taken from the "bedrooms and private homes" of people not suspected of individualised wrongdoing. "[Optic Nerve] continued even after GCHQ became aware that the vast majority had no intelligence value at all," Snowden said.

Snowden made clear he did believe in legitimate intelligence operations. "I would like to clarify I have no intention to harm the US government or strain [its] bilateral ties," he asserted, adding that he wanted to improve government, not bring it down.

The exiled American spy, however, said the NSA should abandon its electronic surveillance of entire civilian populations. Instead, he said, it should go back to the traditional model of eavesdropping against specific targets, such as "North Korea, terrorists, cyber-actors, or anyone else."

Snowden also urged members of the Council of Europe to encrypt their personal communications. He said that encryption, used properly, could still withstand "brute force attacks" from powerful spy agencies and others. "Properly implemented algorithms backed up by truly random keys of significant length … all require more energy to decrypt than exists in the universe," he said.

The international organisation defended its decision to invite Snowden to testify. In a statement on Monday, it said: "Edward Snowden has triggered a massive public debate on privacy in the internet age. We hope to ask him what his revelations mean for ordinary users and how they should protect their privacy and what kind of restrictions Europe should impose on state surveillance."

The council invited the White House to give evidence but it declined.

In the Vanity Fair interview the whistleblower said he paid the bill in the Mira Hotel using his own credit card because he wanted to demonstrate he was not working for a foreign intelligence agency. "My hope was that avoiding ambiguity would prevent spy accusations and create more room for reasonable debate," he told the magazine. "Unfortunately, a few of the less responsible members of Congress embraced the spy charges for political reasons, as they still do to this day."

The NSA says Snowden should have brought his complaints to its own internal oversight and compliance bodies. Snowden, however, insisted he did raise concerns formally, including through emails sent to the NSA's lawyers. "I directly challenge the NSA to deny that I contacted NSA oversight and compliance bodies directly via email," he stated.