Allen has denied wrongdoing. If Allen was found to have had an affair with Kelley, he could face charges of adultery, which is a crime under the Uniform Code of Military Justice.
The Petraeus case has sparked an uproar in Congress, with lawmakers complaining they should have been told earlier about the probe that has roiled the intelligence and military establishment.
Rep. Peter King, R-N.Y., chairman of the House Homeland Security Committee, called the latest revelations in the case "a Greek tragedy."
"It's just tragic," King said Tuesday on NBC's "Today" show. "This has the elements in some ways of a Hollywood movie or a trashy novel."
The issue of what the FBI knew, when it notified top Obama administration officials, and when Congress was told, has brought criticism from lawmakers, who say they should have been told earlier.
The White House wasn't informed of the FBI investigation that involved Petraeus until Nov. 6, Election Day, although agents began looking at Petraeus' actions months earlier, sometime during the summer. Senate Intelligence Committee chairwoman Dianne Feinstein, D-Calif., complained that she first learned of the matter from the media late last week, and confirmed it in a phone call to the then-CIA director on Friday.
That was the same day Obama accepted Petraeus' resignation, and the 60-year-old retired Army general, who headed U.S. military operations in Iraq and Afghanistan before taking charge of the CIA, acknowledged an affair with Broadwell, and expressed regret.
Defending the notification timing, a senior federal law enforcement official pointed Monday to longstanding policies and practices, adopted following abuses and mistakes that were uncovered during the Nixon administration's Watergate scandal of the early 1970s. The Justice Department — of which the FBI is part — is supposed to refrain from sharing detailed information about its criminal investigations with the White House.