The New York Times also reported Sunday that investigators found classified documents on Broadwell's laptop computer. The newspaper cited investigators as saying Petraeus denied he had given them to her.
Retired Gen. James "Spider" Marks, for whom Broadwell once worked and who knows Petraeus, said he doubts security protocols were breached despite what seems an unlikely indiscretion on the part of Petraeus.
"There's almost zero percent chance that national security was compromised or at risk," he said Monday.
A senior U.S. intelligence official said an extramarital affair by a CIA officer is not automatically considered a security violation.
"It depends on the circumstances," the official said.
The official also said Broadwell did not have a security clearance from the CIA.
Another official said Broadwell, who is an officer in the Army reserve, did have some kind of security clearance and that there are no issues with Broadwell having unauthorized access to classified information.
Petraeus' resignation also presents challenges to the congressional inquiry into the Benghazi attack.
CNN has confirmed that Petraeus recently traveled to Libya to meet the CIA station chief to discuss the attack. He was scheduled to testify before a congressional committee this week on the assault and the U.S. government response to it.
That now will not happen, but it is possible that he could be summoned by Congress to testify later.
Some Republicans have criticized the administration's response to the Benghazi attack and have speculated that Petraeus' departure was linked to the congressional inquiry.
Rep. Peter King, R-New York, said elements of the story "don't add up." He called Petraeus "an absolutely essential witness, maybe more than anybody else."
However, a senior U.S. official said Petraeus' departure wasn't connected to the Benghazi hearing.
"Director Petraeus' frank and forthright letter of resignation stands on its own," said the official, who spoke on the condition of anonymity because of the sensitivity of the topic. "Any suggestion that his departure has anything to do with criticism about Benghazi is completely baseless."
Congressional leaders are calling for an explanation of why they weren't notified sooner of the FBI's inquiry when it became clear Petraeus was involved.
Leaders of the House Intelligence Committee are expected to meet Wednesday with acting CIA Director Mike Morell and FBI Deputy Director Sean Joyce to discuss the Petraeus investigation and congressional oversight.
Sen. Diane Feinstein, the Democratic chair of the Senate Intelligence Committee, said on "Fox News Sunday" that she would "absolutely" push for answers.
"I mean, this is something that could have had an effect on national security," she said. "I think we should have been told. There is a way to do it. And that is, just to inform the chair and the vice chairman of both committees, to -- this has happened before, not with precise, same things, but, none of the four of us have ever breached that confidentiality."
On Monday, Feinstein told NBC that her concern about the situation "has actually escalated the last few days."