In the South China Morning Post interview -- published one week after the Guardian revealed the first leaks attributed to Snowden -- he said the agency he once worked for as a contractor typically targets high-bandwidth data lines that connect Internet nodes around the world.
"We hack network backbones -- like huge Internet routers, basically -- that give us access to the communications of hundreds of thousands of computers without having to hack every single one," the newspaper quoted him as saying.
A "backbone" is part of the inner workings of a computer network that links different parts of that network. It is used to deliver data from one part of the network to another and, as such, could expose data from multiple computers if hacked.
'Trying to bully'
While refusing to comment specifically on a person under investigation, White House spokesman Jay Carney explained clearly how and why U.S. authorities consider the leaks to be "very serious."
"They go right to the heart of our efforts to combat terrorism, to combat efforts by extremists who desire to attack the United States and the American people," Carney told reporters Thursday.
FBI Director Robert Mueller offered a similar assessment in testimony before Congress on Thursday.
"These disclosures have caused significant harm to our nation and to our safety," Mueller said. "And we are taking all necessary steps to hold the person responsible for these disclosures."
Snowden hasn't been charged, but he has told The Guardian that he expects the United States to try to prosecute him. He worked for the computer consulting firm Booz Allen Hamilton until Monday, when he was fired after outing himself as the leaker.
Snowden told the South China Morning Post that he felt U.S. officials were pressuring his family and also accused them of "trying to bully" Hong Kong into extraditing him to prevent the release of more damaging information.
He vowed to resist extradition efforts if it comes to that, saying he "would rather stay and fight the United States government in the courts, because I have faith in Hong Kong's rule of law."
"My intention is to ask the courts and people of Hong Kong to decide my fate," the South China Morning Post quoted Snowden as saying. "I have been given no reason to doubt your system.''
But Hong Kong lawmaker Regina Ip, a former secretary of security for the territory, said Tuesday that while any extradition process could take months, Snowden isn't necessarily beyond the reach of the United States.
"If he thought there was a legal vacuum in Hong Kong which renders him safe from U.S. jurisdiction, that is unlikely to be the case," she said.
Legal experts says that Beijing can get involved in the process to extradite a person from Hong Kong if the case significantly affects defense or foreign affairs.
But some observers say that Chinese authorities are unlikely to want to rock the boat in this instance.
"Given the somewhat fraught Hong Kong-Beijing relationship, the political impact of Beijing interference in this Hong Kong legal matter could be grave," the Beijing-based analyst and blogger, Bill Bishop, wrote in an article for USA Today.
The newspaper said Snowden has been hiding in undisclosed locations in Hong Kong since checking out of his hotel room Monday, a day after he revealed his identity in an interview with The Guardian.
Snowden told the Morning Post he is not trying to evade U.S. authorities.
"People who think I made a mistake in picking Hong Kong as a location misunderstand my intentions," the newspaper quoted him as saying. "I am not here to hide from justice; I am here to reveal criminality."
The NSA and the national intelligence director did not immediately respond to a CNN request for comment.
Asked during a media briefing Wednesday for comment on Snowden's latest claims, U.S. State Department spokeswoman Jennifer Psaki declined. She said she had not seen the latest South China Morning Post report.