Even before the F.B.I. conducted 550 interviews of officials and seized the phone records of Associated Press reporters in a leak investigation connected to a 2012 article about a Yemen bomb plot, agents had sought the same reporters’ sources for two other articles about terrorism. In a separate case last year, F.B.I. agents asked the White House, the Defense Department and intelligence agencies for phone and e-mail logs showing exchanges with a New York Times reporter writing about computer attacks on Iran. Agents grilled officials about their contacts with him, two people familiar with the investigation said. And agents tracing...