President Barack Obama has put a promotion nomination for Allen on hold.

Kelley’s emails triggered the eventual downfall of Petraeus and placed others under scrutiny. Kelley knew Petraeus and Allen from the Tampa social scene when they were stationed at nearby MacDill Air Force Base. It was there that the mid-level White House aide who hosted her at the Executive Mansion met her, said the White House official.

Broadwell attended two meetings in the White House’s executive office building. In 2009 she met with a member of Obama’s national security staff and in June 2011 she joined about 20 people for a briefing on Afghanistan and Pakistan policy, the official said. The 2011 meeting was just a few hours before Obama gave a prime-time speech about withdrawing troops from Iraq.

Petraeus, in his first media interview since he resigned, told CNN this week that he had never given classified information to Broadwell. She has said she didn’t receive such material from Petraeus.

But the FBI found a substantial number of classified documents on Broadwell’s computer and in her home, according to the law enforcement official, and is investigating how she got them. The Army has now suspended her security clearance.

The official outlined new details Friday of the timing of the FBI investigation that showed that agents spent the summer making certain that no one had hacked into Petraeus’ computers to track his movements — a potential national security vulnerability raised by some of the first emails they saw in the case. They also used the summer to rule out any possibility he somehow participated in harassing Kelley by email.

After that, in early fall, Broadwell was interviewed by the FBI and agents searched her computers and found substantial amounts of classified documents, the law enforcement official said. The focus of the investigation shifted and agents spent most of October working with the Pentagon to determine where she got the documents, their significance and her right to have them.

The CIA on Thursday opened an exploratory investigation into Petraeus’ conduct. The inquiry ‘‘doesn’t presuppose any particular outcome,’’ said CIA spokesman Preston Golson. At the same time, Army officials say that, at this point, there is no appetite for recalling Petraeus to active duty to pursue any adultery charges against him.

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