Republican and Democratic senators on Tuesday called for scandal-plagued CIA ex-director David Petraeus to testify about the deadly September 11 attack on the US mission in Benghazi, Libya.

"I believe he will (testify). I think he's a responsible person, and I believe he will come," Democrat Dianne Feinstein, chair of the Senate Select Committee on Intelligence, said on CNN.

"So we are going to try to set that up today because his view as someone who was actually there... I think that's important for us to hear."

In the first congressional work week since the re-election of President Barack Obama, lawmakers had expected all eyes to be focused on several year-end fiscal challenges such as expiring tax breaks and across-the-board budget cuts.

But Benghazi -- and scandals that have rocked Obama's national security team -- are suddenly on the front burner. There are no fewer than five congressional hearings this week, most of them closed-door sessions, on what happened in Libya.

Feinstein and the intelligence committee's ranking Republican, Saxby Chambliss, met later Tuesday with CIA acting director Michael Morell, who arrived in the US Capitol with a large security detail that prevented reporters from approaching him.

Morell was expected to replace Petraeus in a number of the hearings, and CBS News reported he was to attend a House Intelligence Committee briefing on the FBI investigation that led to Petraeus's departure.

Petraeus resigned last week when he admitted to having an affair with a married military reservist and author of a fawning biography of the general.

Despite that scandal, lawmakers see Petraeus as potentially vital to their probe into exactly what happened in Benghazi on September 11 when four Americans were killed including US ambassador Christopher Stevens.

Republican Marco Rubio, who sits on the Senate's intelligence and foreign affairs committees, emerged from a classified briefing by the latter body to say there were many unanswered questions and that he hoped Petraeus and Secretary of State Hillary Clinton would testify on the Libya attack.

"She has an invaluable role to play," Rubio told reporters. "I think we need to hear from David Petraeus as well."

Rubio said he and others wanted to know why the Obama administration delayed in acknowledging the incident in Benghazi as a terrorist attack.

He specifically addressed how Obama's UN ambassador Susan Rice went on TV talkshows five days after the Benghazi attack to describe the incident as a protest against an anti-Islam video that spun out of control.

"I don't think there is any reasonable doubt now that this was not a protest gone violent. This was an attack, by well armed, military-style individuals," Rubio said.

"What is real important to know is why did they wait so long... to publicly change their position on it."

Dick Durbin, the Senate's number three Democrat, said the Senate Foreign Relations Committee in its closed-door hearing received a "detailed chronology in terms of what happened on September 11," but would not go into details of events or materials shared with lawmakers.

Retiring Republican Senator Olympia Snowe also said she hoped Petraeus would testify on Capitol Hill.

"Absolutely, I think it would be critical to our efforts in the Senate Intelligence Committee" if Petraeus were to testify, Snowe told reporters.

"My understanding is he visited Benghazi to get firsthand an account and appraisal of the circumstances surrounding the horrific events on September 11."

Republican Senator James Risch, who like Rubio sits on both the intelligence and foreign relations committees, said major questions about Benghazi remained.

"We're hearing explanations, but there's a lot of us I think who want clearer explanations than what we're getting," Risch said.