In an interview with the South China Morning Post in Hong Kong, Snowden said the National Security Agency has attacked the computers of non-military targets, including Chinese public officials, businesses, academics and students, since 2009.
Snowden said he believes there are more than 61,000 hacking operations worldwide, the Post said.
"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," Snowden told the Post.
Snowden defended his actions in revealing the U.S. secret telephone metadata-gathering program.
"I'm neither traitor nor hero. I'm an American," he told the Post.
Interviewed in Hong Kong, Snowden said he picked the city because "I am not here to hide from justice; I am here to reveal criminality."
A Gallup poll Wednesday showed a majority of Americans disapprove of the federal government's domestic telephone data mining program by a 53 percent to 37 percent margin.
The Princeton, N.J., polling company conducted its survey Monday and Tuesday. Democrats (49 percent) were more likely to approve of the surveillance than Independents (34 percent) or Republicans (32 percent).
Gallup didn't provide a margin of error in its release.
Hong Kong has an extradition treaty with the United States, but Snowden vowed to fight any attempt to send him to America for trial.
"My intention is to ask the courts and people of Hong Kong to decide my fate," he said.
CBS reported Snowden had left Hong Kong.
Former Rep. Ron Paul, R-Texas, told Fox News Tuesday he feared Snowden would be targeted for assassination by a cruise missile or a drone rocket.
"I mean, we live in a bad time where American citizens don't even have rights and that they can be killed, but the gentleman is trying to tell the truth about what's going on," CBS quoted Paul as saying.
In the wake of the revelations, high-tech giants this week called on Washington to make public more information about the spying programs and lift gag orders about Internet data collection.
The requests were made by Google Inc., Facebook Inc., Microsoft Corp. and Yahoo! Inc. and echoed by a top Twitter Inc. official.
The requests came as the Senate Intelligence Committee asked the National Security Agency, whose sweeping Internet surveillance program is at the center of the controversy, to publicly explain its programs that use phone and Internet records "so that we can talk about them," said committee Chairwoman Dianne Feinstein, D-Calif., who has defended the surveillance efforts.
At the same time, a bipartisan group of eight senators announced a bill to declassify the secret U.S. Foreign Intelligence Surveillance Court opinions that give the NSA the legal power to carry out the sweeping Internet surveillance programs.
"Americans deserve to know how much information about their private communications the government believes it's allowed to take under the law," said bill author Sen. Jeff Merkley, D-Ore.
Merkley originally introduced the bill in December, but it went nowhere.
The calls for greater transparency followed reports by British newspaper The Guardian and The Washington Post last week the NSA collects and analyzes millions of people's data from nine U.S. Internet companies.
The newspapers said the program, code-named PRISM, was focused on foreigners. But they said the NSA has also collected data on U.S. citizens and residents that under certain circumstances can be reviewed by officials.
"Google has nothing to hide," Chief Legal Officer David Drummond wrote, saying allowing the information to become public would let Google significantly expand its semi-annual "transparency reports" about information sought by courts and police worldwide.
The Justice Department said it was reviewing Google's request.
Facebook issued a statement shortly after Google made its letter public, saying it might start its own "transparency reports" -- a move the Post said Facebook had long resisted.
"We urge the United States government to help make that possible by allowing companies to include information about the size and scope of national security requests we receive, and look forward to publishing a report that includes that information," Facebook General Counsel Ted Ullyot wrote.
Microsoft issued a statement in support of Google, saying greater transparency "would help the community understand and debate these important issues."
Yahoo! said, "We recognize the importance of privacy and security, and we also believe that transparency ... will help build public trust."
Twitter General Counsel Alex Macgillivray, who previously was a Google lawyer, posted on his Twitter account: "Completely agree with @Google, @SenJeffMerkley & others -- we'd like more NSL transparency and @Twitter supports efforts to make that happen."