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Rep. Peter T. King, New York Republican and chairman of the Homeland Security subcommittee on counterterrorism and intelligence, demanded Mr. Snowden’s extradition. “The United States government must prosecute him to the fullest extent of the law,” Mr. King said in a statement.

Mr. Snowden’s latest employer, defense contractor Booz Allen Hamilton, promised in a statement to cooperate with any investigation.

The U.S. and Hong Kong signed an extradition treaty in 1996, a year before the former British colony was returned to China as a special administrative region. It allows for the exchange of criminal suspects in a process that also may involve the Chinese government, which has been widely accused of engaging in cyberespionage.

Under the treaty, Hong Kong authorities can hold Mr. Snowden for 60 days after a U.S. request that includes probable cause for his extradition. But Beijing could order Hong Kong officials not to surrender Mr. Snowden, citing “defense, foreign affairs or essential public interest or policy” reasons, per the treaty.

The Chinese also could refuse to turn over Mr. Snowden to U.S. authorities if they believe an extradition request is “politically motivated” or is designed to punish a suspect for “political opinion,” or if they believe complying would deny him a fair trial, according to the treaty.

According to The Associated Press in Hong Kong, Mr. Snowden checked out of the Mira Hotel on Monday and his whereabouts was unknown.

Glenn Greenwald, the columnist at The Guardian who first reported the NSA and Prism programs last week and who profiled and identified Mr. Snowden, the former intelligence contractor “doesn’t really trust the judicial system in the United States to give him a fair trial.”

“I think if he trusted the political system and the political culture in the United States he would have just remained there and said ‘I did what I did and I want to defend it,’” Mr. Greenwald said.

The NSA and Prism flaps will affect U.S. foreign relations on another front — with privacy-conscious governments in Western Europe, many of whose citizens use such Prism-targeted American companies as Google and Apple for Internet and related services.

German government spokesman Steffen Seibert told reporters in Berlin on Monday that Chancellor Angela Merkel would raise the programs with Mr. Obama when he visits Berlin on June 18. Germany’s Interior Ministry said it had queried U.S. officials on the programs’ effect on German citizens.

Support was growing for Mr. Snowden in other quarters, including an online forum operated by the White House. More than 26,000 people had signed a petition for Mr. Obama to pardon Mr. Snowden by 5 p.m. Monday, a day after the petition was created.

Edward Snowden is a national hero and should be immediately issued a full, free and absolute pardon for any crimes he has committed or may have committed related to blowing the whistle on secret NSA surveillance programs,” the petition states.

The White House doesn’t respond to petitions with fewer than 100,000 signatures, but the petition for Mr. Snowden was relatively popular. Another petition, requesting that alleged WikiLeaks suspect Bradley Manning be set free, has collected about 1,600 signatures in the week since it was posted on the White House site.