Feinstein says she'll push for Petraeus to testify

(CNN) -- Sen. Dianne Feinstein, Senate Intelligence Committee chairwoman, said she hopes to talk to Gen. David Petraeus and will urge him to testify on the Benghazi, Libya attacks as previously scheduled.

"I believe he will. I think he's a responsible person and I believe he will come. We are going to try to set that up today," she said in an interview to air Tuesday on CNN's "The Situation Room with Wolf Blitzer."

Feinstein said the former CIA director's testimony is relevant because news of his extramarital affair broke after his recent trip to Libya, where he discussed the violence and other issues with the CIA station chief there.

In a separate interview with CNN Senior Congressional Correspondent Dana Bash, Feinstein said Tuesday the committee could call Petraeus to appear on Capitol Hill as early as Friday morning, adding that his lack of testimony would be a very big stone left unturned.

Feinstein told CNN that she and Sen. Saxby Chambliss, the vice chairman of the committee, plan to meet with Michael Morell, the acting director of the CIA who took over after Petraeus resigned Friday, and other intelligence officials as part of an "inquiry" into September's U.S. consulate attack in Libya that killed four Americans.

"(Petraeus) was actually in Benghazi, and actually spoke to people involved in the incident. I think that's important for us to hear," she said on "The Situation Room."

She later added: "There's only one way to ascertain (his trip), and that is to talk directly with Petraeus and do it in a classified setting with the committee present."

The California senator has been vocal in her disappointment of the Federal Bureau of Investigation for its handling of the Petraeus scandal, as well as a second investigation involving Gen. John Allen, the top U.S. commander in Afghanistan, and "potentially inappropriate" e-mails he exchanged with Jill Kelley, a close family friend of Petraeus.

Feinstein questioned why the FBI did not notify oversight committees in Congress about the investigations beforehand, given that classified information could be at risk.

"It's rather shocking to find out candidly that we weren't briefed and that we find out from the press in the way in which we did, with no heads up, with no opportunity to ask questions, or put together any information," she said. "So we have been coming from behind on this."

She continued: "I have many questions about the nature of the FBI investigation, how it was instituted, and we'll be asking those questions."