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Gen. Alexander said that when the NSA comes across a U.S. connection to an overseas terrorist plot, it turns over the case to the FBI.

NSA may not target the phone calls or emails of any U.S. person anywhere in the world without individualized court orders,” he said. The term “U.S. person” includes all citizens, legal immigrants and U.S. corporations.

Deputy Attorney General James Cole noted that “countries and allies of ours all over the world collect intelligence. We all know this.”

But the U.S. system is more “transparent [than] many of our partners, many in the EU, countries like France, the U.K., Germany, who we work with regularly,” he said.

As evidence, he cited a recent white paper by the Hogan Lovells law firm, which he said found that U.S. rules, based on the Foreign Intelligence Surveillance Act, “impose at least as much if not more due process and oversight on foreign intelligence surveillance than other countries — and this includes EU countries.”

The United States is also “much more transparent about its procedures,” he said.

The stakes were high Tuesday, as officials attempted to explain the details of classified programs — only parts of which had been exposed. They said they were treading a fine line between releasing enough information to reassure Americans without initiating further damaging disclosures that might help terrorists or foreign spies evade surveillance.

Rep. Mike Rogers, Michigan Republican and committee chairman, called it “frustrating … sitting at the intersection of classified intelligence programs and transparent democracy as representatives of the American people.”

Officials have disclosed details of two U.S. plots that they said had been detected and stopped with the help of intelligence from the NSA’s collection programs. Najibullah Zazi, who schemed to bomb the New York subway, and David Headley, who helped plan the 2008 Mumbai massacre, were caught because of their telephone or online communications with al Qaeda suspects abroad, officials said last week.

FBI Deputy Director Sean Joyce revealed two more plots that he said had been disrupted with the help of intelligence from the two programs.

In one, a “known extremist in Yemen” was being monitored using Prism. The extremist was in contact with a man in Kansas City named Khaled Ouazzani.

“We went up on electronic surveillance and identified his co-conspirators” in plotting to bomb the New York Stock Exchange, said Mr. Joyce. “We were able to disrupt the plot, we were able to lure some individuals to the United States, and we were able to effect their arrest. And they were convicted for this terrorist activity.”

In the second instance, the FBI in October 2007 reopened a cold case from 2001, after “the NSA provided us a telephone number only in San Diego that had indirect contact with an extremist outside the United States.”

Gen. Alexander said that classified details of all 50-plus cases would be delivered to Congress on Wednesday and that the administration would work to declassify more of the programs’ successes.