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Construction trailers sit in front of the new National Security Agency (NSA) data center June 10, 2013 in Bluffdale, Utah.

Privacy groups said they were delighted with the support for the bill. "This is a historic turn of events in our government's approach to counterterrorism policies," Laura Murphy, director of the American Civil Liberties Union's Washington Legislation Office, said in a statement.

The legislation still faces several hurdles before becoming law, including winning the approval of a majority in the full House, as well as backing in the U.S. Senate. It is similar to NSA reforms proposed by President Barack Obama.

The House Intelligence Committee will debate and vote on its somewhat less restrictive version of the package on Thursday, which could set up a standoff on the House floor.

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Democratic Sen. Patrick Leahy, the chairman of the Senate Judiciary Committee, applauded the House committee's action, although he said he wished it had gone further, such as including a strong special advocate in the secret court that oversees NSA surveillance programs.

Signaling that the fight over the surveillance programs is not over, Leahy said in a statement that he would push for those reforms when his committee considers the legislation, known as the USA Freedom Act, this summer.

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NSA data collection overhaul advances