The revelation threatens to fell another of the US military's biggest names and suggests the scandal involving Mr Petraeus – a retired four-star general who held Mr Allen's job in Afghanistan before moving to the CIA last year – could expand.
A US official said the FBI uncovered between 20,000 and 30,000 pages of communications – mostly emails spanning from 2010 to 2012 – between Mr Allen and Jill Kelley. She has been identified as a long-time friend of the Petraeus family and a Tampa, Florida, volunteer social liaison with military families at MacDill Air Force Base.
It was Mrs Kelley's complaints about harassing emails from the woman with whom Mr Petraeus had an extramarital affair, Paula Broadwell, that prompted an FBI investigation that disclosed Mr Petraeus's involvement with Mrs Broadwell. Mr Petraeus resigned from the CIA post on Friday.
Asked whether there was concern about the disclosure of classified information, the official said: "We are concerned about inappropriate communications. We are not going to speculate as to what is contained in these documents."
Defence Secretary Leon Panetta said he had asked that Mr Allen's nomination to be Commander of US European Command and Supreme Allied Commander Europe be delayed.
President Barack Obama has put the nomination on hold, the White House said yesterday.
Mr Allen, who is now in Washington, was due to face a Senate confirmation hearing tomorrow, as was his successor in Afghanistan, General Joseph Dunford.
The FBI referred the case to the Pentagon on Sunday and Mr Panetta directed the Defence Department's inspector general to handle the investigation.
The US defence official said Mr Allen denied wrongdoing and that Mr Panetta had opted to keep him in his job while the matter was under review.
"While the matter is under investigation and before the facts are determined, General Allen will remain commander of ISAF," Mr Panetta said, referring to the Nato-led force in Afghanistan.
Earlier, Mr Panetta said he was reviewing Mr Allen's recommendations on the future US presence in Afghanistan after most troops withdraw by the end of 2014.
Commending Mr Allen's leadership in Afghanistan, Mr Panetta said: "He is entitled to due process in this matter."
Evidence that the case involving Petraeus was not fully closed came on Monday when FBI agents searched the Charlotte, North Carolina, house of Mrs Broadwell. Agents entered the house carrying boxes at around 9pm and about four hours later took away what appeared to be two computers and about 10 boxes.
Mrs Broadwell co-wrote a biography of the decorated former general, and some have questioned whether she obtained classified information from him.
The FBI investigation of the emails received by Kelley traced them to Mrs Broadwell and subsequently uncovered emails that revealed the affair. The emails between the two women were of a "childish", jealous nature and showed some one-upmanship of trying to come across as being more important to Petraeus, the official said.