Timothy Edgar, a former intelligence official in the Bush and Obama administrations, said that the rule concerning collection “about” a person targeted for surveillance rather than directed at that person had provoked significant internal discussion.

“There is an ambiguity in the law about what it means to ‘target’ someone,” Mr. Edgar, now a visiting professor at Brown, said. “You can never intentionally target someone inside the United States. Those are the words we were looking at. We were most concerned about making sure the procedures only target communications that have one party outside the United States.”