"...A decision was made somewhere not to brief us, which is atypical," Feinstein said. "This is certainly an operationally sensitive matter. But we weren't briefed. I don't know who made that decision."
According to a source with knowledge of the e-mails, the messages accused Kelley of untoward behavior with some generals at MacDill Air Force Base in Tampa, Florida where Kelley did volunteer work.
The e-mails detailed the "comings and goings of the generals and Ms. Kelley," said the source, who declined to speak on the record because of sensitivity of the investigation.
Among those believed to be referenced in the e-mails was Petreaus. Because parts of Petreaus' schedule were not public, the e-mails raised questions about whether the sender of the e-mails had access to his private schedule or other sensitive information.
The content of the e-mails was first reported by NBC News.
At one point, Petraeus told Broadwell to stop sending the e-mails, a U.S. official said. It was not clear whether his request was made during or after his affair with Broadwell.
During the investigation, other communications surfaced between Petraeus and Broadwell, a married mother of two, according to a U.S. official.
Petraeus used a personal account to e-mail Broadwell, not his CIA account, a U.S. official said.
The FBI interviewed Petraeus, said the official, who stressed that the CIA director was never the target of the investigation and his communications were never compromised.
Broadwell was interviewed twice by the FBI, a U.S. official said.
The official said the investigation is not officially closed, but it appeared there will be no charges.
According to a congressional aide familiar with the matter, the House and Senate intelligence committees weren't informed that there was an FBI investigation into the situation until Friday.
"The committees are required to be kept informed of significant intelligence activities," the aide said Saturday. "If there was an official investigation that was looking, at least in part, at information that was compromising the CIA director, then I think there's a solid argument to say that the committee leadership should have been notified to at least some level of detail."
But former FBI assistant director Tom Fuentes told CNN on Monday that if, as the investigation progresses, the FBI is not "uncovering criminal activity" or a "breach of security" then "there really isn't a need" to notify members of Congress.
The FBI has "very strict protocols" about who should be notified in this type of investigation, Fuentes said.
House Majority Leader Eric Cantor, R-Virginia, knew in October about Petraeus' involvement in an extramarital affair, a spokesman for the congressman told CNN on Sunday.
Doug Heye said Cantor was tipped to the information by an FBI employee. The congressman had a conversation with the official, described as a whistle-blower, about the affair and national security concerns involved in the matter, he said.