Washington (CNN) -- An angry Dianne Feinstein, the Senate Intelligence Committee chairwoman, warned again Monday she would investigate why the FBI did not notify oversight committees about its investigation into CIA Director David Petraeus after the bureau determined he was having a secret and risky extramarital affair.
"... A decision was made somewhere not to brief us, which is atypical," the California Democrat told NBC's Andrea Mitchell about how the top Democrats and Republicans on the House and Senate intelligence committees are usually briefed on key developments. "This is certainly an operationally sensitive matter. But we weren't briefed. I don't know who made that decision."
Section 501 of the National Security Act of 1947 spells out the requirements for the executive branch to inform the congressional intelligence committees of key intelligence-related activities.
"The president shall ensure that the congressional intelligence committees are kept fully and currently informed on the intelligence activities of the United States, including any significant anticipated intelligence activity as required by this title," the statute reads.
Feinstein described the unfolding scandal, which she first learned about on Friday when Petraeus announced publicly his resignation, "like peeling an onion. Every day another peel comes off, and you see a whole new dimension to this."
"My concern has actually escalated the last few days," she said.
On Sunday, she told Fox News an investigation of the FBI was needed because the illicit affair "could have had an effect on national security."
One specific national security concern deals with whether Paula Broadwell, the woman with whom Petraeus had an affair, was privy to classified information. In a speech at the end of October, Broadwell suggested the terrorist attack on the U.S. Consulate in Benghazi, Libya, took place because the U.S. was housing Libyan prisoners there -- a theory, she noted at the time, that had not been vetted yet.
"I do not know how she got that information," Feinstein said. "We should find out." The claim by Broadwell has since been discounted by administration officials.
Feinstein also was incensed that an FBI whistle-blower -- who may have feared the investigation into Petraeus wasn't proceeding properly -- had complained to the office of House Majority Leader Eric Cantor, R-Virginia, who then was aware of the investigation even before President Barack Obama was informed.
Feinstein's committee will meet privately Tuesday to determine how it will proceed on the FBI matter.
It is important "that we have an orderly process, that we not jeopardize anyone's rights, that we be respectful," she said, adding that some of the investigation will be done in public and some of it will be behind closed doors.
Separately, the committee is conducting an investigation into the fatal attack on the consulate in Benghazi. Petraeus was to testify before a closed hearing Thursday into the attack, but he will now be replaced by Acting CIA Director Mike Morell.
"Disciplinary action" could be in order, Feinstein said.
Feinstein said she wants to read a "trip" report that she was told Petraeus filed on his just-concluded visit to Benghazi, where he personally investigated the circumstances of the attack. But after a second person told her the report had not been written yet, Feinstein warned she would move to have it subpoenaed if necessary.
She said also that Petraeus will testify before the committee on Benghazi at some point, probably in closed session.