WASHINGTON — The U.S. foiled a plot to bomb the New York Stock Exchange because of the sweeping surveillance programs at the heart of a debate over national security and personal privacy, officials said Tuesday at a rare open hearing on intelligence — a set-piece for supporters of the spying.

The House Intelligence Committee, led by lawmakers sympathetic to the extraordinary surveillance, provided a venue for officials to defend the once-secret programs. There was limited probing of claims that the collection of people’s phone records and Internet usage has disrupted dozens of terrorist plots, and few details were volunteered.

Army Gen. Keith Alexander, director of the National Security Agency, said the two recently disclosed programs — one that gathers U.S. phone records and another that is designed to track the use of U.S.-based Internet servers by foreigners with possible links to terrorism — are critical.

Alexander said after the hearing that most of the documents accessed by Edward Snowden, a former systems analyst on contract to the NSA, were on a Web forum available to many NSA employees.

Intelligence officials last week disclosed some details on what they said were two thwarted attacks, one targeting the New York subway system, one a Danish newspaper office that had published the cartoon depictions of the Mohammad. On Tuesday, Alexander said more than 50 terrorist acts were averted because of the surveillance programs in question.

In one example, Joyce said the NSA was able to identify an extremist in Yemen who was in touch with Khalid Ouazzani in Kansas City, Mo., enabling authorities to identify co-conspirators and thwart a plot to bomb the New York Stock Exchange.

Ouazzani pleaded guilty in May 2010 in federal court in Missouri to charges of conspiracy to provide material support to a terrorist organization, bank fraud and money laundering.

Joyce also said a terrorist financier in San Diego was identified and arrested in October 2007 because of a phone record provided by the NSA.

The individual was making phone calls to a known designated terrorist group overseas, Joyce said.

Alexander said the Internet program had helped stop 90 percent of the 50-plus plots he cited.