A top-secret National Security Agency hacking unit infiltrates computers around the world and breaks into the toughest data targets, according to internal documents quoted in a magazine report on Sunday.

Details of how the division, known as Tailored Access Operations (TAO), steals data and inserts invisible "back door" spying devices into computer systems were published by the German magazine Der Spiegel.

The magazine portrayed TAO as an elite team of hackers specialising in gaining undetected access to intelligence targets that have proved the toughest to penetrate through other spying techniques, and described its overall mission as "getting the ungettable". The report quoted an official saying that the unit's operations have obtained "some of the most significant intelligence our country has ever seen".

NSA officials responded to the Spiegel report with a statement, which said: "Tailored Access Operations is a unique national asset that is on the front lines of enabling NSA to defend the nation and its allies. [TAO's] work is centred on computer network exploitation in support of foreign intelligence collection."

Der Spiegel has previously reported on documents leaked by the former NSA contractor Edward Snowden. The report on Sunday was partly compiled by Laura Poitras, who collaborated with Snowden and the Guardian on the first publication of revelations about the NSA's collection of the telephone data of thousands of Americans and overseas intelligence targets.

On Friday, the NSA phone data-collection programme was ruled legal by a federal judge in New York, days after a federal judge in Washington declared the operations unconstitutional and "almost Orwellian".

On Sunday, appearing on the CBS talk show Face the Nation, former air force general and NSA and CIA chief Michael Hayden called Snowden a traitor and accused him of treason. He also accused Snowden of making the NSA's operation "inherently weaker" by revealing not just the material that comes out of the agency but the "plumbing", showing how the system works inside the government.

On NBC's Meet the Press Ben Wizner, a legal adviser to Snowden, said the contrasting opinions of the two federal judges were now likely to see the case end up in front of the supreme court.

"It's time for the supreme court to weigh in and to see whether, as we believe, the NSA allowed its technological abilities to outpace democratic control," Wizner said.

Asked if Snowden, who was granted one year's asylum in Russia, should return to the US to face charges, Wizner said: "For now, he doesn't believe and I don't believe that the cost of his act of conscience should be a life behind bars."

In a recent interview with the Washington Post, Snowden declared that he had "already won" and accomplished what he set out to do. On Sunday, Wizner said Snowden's mission was to bring the public, the courts and lawmakers into a conversation about the NSA's work.

"He did his part," Wizner said. "It's now up to the public and our institutional oversight to decide how to respond."

According to the Spiegel report, TAO staff are based in San Antonio, Texas, at a former Sony computer chip factory, not far from another NSA team housed alongside ordinary military personnel at Lackland Air Force Base. The magazine described TAO as the equivalent of "digital plumbers", called in to break through anti-spying "blockages". The team totalled 60 specialists in 2008, the magazine said, but is expected to grow to 270 by 2015.

TAO's areas of operation range from counter-terrorism to cyber attacks, the magazine said, using discreet and efficient methods that often exploit technical weaknesses in the technology industry and its social media products.

The documents seen by Der Spiegel quote a former chief of TAO saying that the unit "has access to our very hardest targets" and its mission would be to "support computer network attacks as an integrated part of military operations" using "pervasive, persistent access on the global network".