The FBI probe into the sex scandal that prompted CIA Director David Petraeus to resign has expanded to ensnare Gen. John R. Allen, the commander of US and NATO troops in Afghanistan, the Pentagon announced early Tuesday.

According to a senior U.S. defense official, the FBI has uncovered between 20,000 and 30,000 documents — most of them e-mails — of “potentially inappropriate” communication between Allen and Jill Kelley, the 37-year-old Tampa woman whose report of harrassment by a person who turned out to be Petraeus’s mistress ultimately led to Petraeus’s downfall.