Washington—The top Senate Democrat on intelligence issues said Sunday she would investigate the Federal Bureau of Investigation’s handling of the inquiry into Central Intelligence Agency chief David Petraeus, including why top lawmakers weren’t informed of the investigation before it became public.

Associated PressDavid Petraeus, shown in September, resigned as CIA chief suddenly on Friday, saying he had an extramarital affair.

CIA Director David Petraeus resigned as head of the intelligence agency, saying he “showed extremely poor judgment” by engaging in an extramarital affair. Neil King has details on The News Hub. Photo: AFP/Getty Images.

Sen. Dianne Feinstein (D., Calif.), the chairwoman of the Senate Select Committee on Intelligence, said on “Fox News Sunday” that she learned of the Petraeus investigation on Friday when her staff began getting press inquiries on the matter. She said she and other committee leaders are routinely made aware of investigations involving national security issues prior to them becoming public.

“We received no advance notice” of the inquiry involving Mr. Petraeus, said Sen. Feinstein. “It was like a lightning bolt.” She later added: “This is something that could have had an effect on national security. I think we should have been told.”

The Petraeus matter, stemming from an extramarital affair that led to his resignation, will be taken up during a previously scheduled hearing before her committee this week, she said. The hearing will focus on the Sept. 11 attack on the U.S. consulate in Libya.

Felled by Scandal

There is a long list of leaders felled by allegations of personal or ethical lapses in recent years, including the CIA’s David Petraeus and Lockheed Martin’s Christopher Kubasik.

Sen. Feinstein said her committee may ask Mr. Petraeus to testify before Congress. Sen. Feinstein also dismissed speculation that Mr. Petraeus’s investigation was linked to fallout from the Libya attack.

Meanwhile, House Homeland Security Committee Chairman Peter King (R., N.Y.) called for an investigation into whether the FBI took too long to disclose its findings to the National Security Council and President Barack Obama.

“It just doesn’t add up, the whole time line here,” Mr. King, who also serves on the House Permanent Select Committee on Intelligence, said Sunday on CNN’s “State of the Union” program. “The president should have been informed at the earliest point.”

Mr. Petraeus stepped down suddenly on Friday, saying he had an extramarital affair. The affair was discovered by the FBI during an investigation into potentially harassing emails sent by a woman romantically linked to Mr. Petraeus to a second woman, according to people familiar with the matter.

The FBI and prosecutors in North Carolina and Florida began their investigation last spring. Initially, they looked at the possibility that someone had hacked into Mr. Petraeus’s emails but later determined no cyber-breach had occurred.

The FBI and Justice Department informed the Director of National Intelligence, James Clapper, of their findings early last week. Mr. Clapper informed Obama administration officials on Wednesday.