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Snowden made the allegations in his first comments since revealing his identity as the man behind the leaks about the US National Security Agency (NSA) spying, according to the Guardian.
The whistleblower, who has fled from the US to Hong Kong, also accused the US of bullying the territory to extradite him because it did not want local authorities to learn of its cyber activities, the paper said.
As the US increases pressure on China to halt its cyber espionage activities, Snowden claims that the US has hacked hundreds of targets in China as part of more than 61,000 NSA hacking operations globally.
Snowden claims the NSA hacks network backbones or huge internet routers that enable access to hundreds of thousands of computers without having to hack every single one.
His allegations appear to back up China’s claims that it had "mountains of data" on cyber attacks by the US.
In a statement, the US State Department said: "There is a difference between going after economic data and the issues of surveillance that the president has addressed, which are about trying to stop people doing us harm.”
Meanwhile, NSA director Keith Alexander has appeared before a US Senate hearing to defend his agency’s internet and telephone data surveillance programmes.
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He said the programmes had disrupted dozens of terror plots, according to the BBC.
Alexander said intelligence officials would brief the Senate intelligence committee behind closed doors, but some details would remain classified to avoid jeopardising national security.
European justice officials have expressed concerns over the US surveillance programmes and have demanded to know whether the privacy rights of EU citizens have been infringed.
In a news conference with UK foreign secretary William Hague in Washington DC, US secretary of state John Kerry said both countries understood the "delicate but vital balance" between privacy and security.
"With respect to privacy, freedom and the Constitution, I think over time this will withstand scrutiny and people will understand it," he said.
Intelligence officials have insisted agents do not listen in on telephone conversations and that the Prism internet monitoring programme targets only non-US citizens outside the US.
Hague has attempted to quell concerns about the UK’s alleged access to the Prism programme by insisting that UK intelligence agencies operate within the law and a comprehensive system of checks and balances.