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Mr. Snowden said Tsinghua University in Beijing and Chinese University in Hong Kong, home of some of the country’s major Internet traffic hubs, were targets of extensive hacking by U.S. spies this year. He said the NSA was focusing on so-called “network backbones” in China, through which enormous amounts of Internet data passes.

The Chinese government has not commented on the extradition request and Mr. Snowden’s departure, but its state-run media have used Mr. Snowden’s allegations to poke back at Washington after the U.S. had spent the past several months pressuring China on its international spying operations.

A commentary published Sunday by the official Xinhua News Agency said Mr. Snowden’s disclosures of U.S. spying activities in China have “put Washington in a really awkward situation.”

“Washington should come clean about its record first. It owes … an explanation to China and other countries it has allegedly spied on,” it said. “It has to share with the world the range, extent and intent of its clandestine hacking programs.”

• Sylvia Hui in London and Lynn Berry in Moscow contributed to this article.