A rancorous feud between Republicans and President Barack Obama over the deadly attack on the US mission in Libya has moved to Congress, where lawmakers have summoned senior figures to testify.

Fallen spy chief David Petraeus, who resigned last week after confessing to an extramarital affair, is to face closed door hearings of the Senate and House intelligence committees on Friday, officials said.

That sets up a compelling end to a whirlwind week in which Washington digested the CIA director's shock resignation, and Republicans called for "Watergate-style" hearings on the September 11 Benghazi attack.

And the pain is to continue for the administration, with Secretary of State Hillary Clinton agreeing to attend later in the year.

On Wednesday, Senators John McCain and Lindsey Graham accused Obama of a major failure of leadership before, during and after the attack on the Benghazi consulate, in which four Americans including Ambassador Chris Stevens died.

The shots continued Thursday, from House Republicans who drilled into the "arrogance and dishonesty" of the administration's handling of the crisis.

Republican lawmakers have accused the administration of failing to explain why there was inadequate security at the compound and why it took several days to provide a coherent account of the attack, blamed on Islamist militants.

Ileana Ros-Lehtinin, chairwoman of the House Foreign Affairs Committee, which held the only open-door hearing of the week on Benghazi, blasted the "disgraceful... sad parade of conflicting accounts of the attack that we have received from administration officials."

All eyes will be on Petraeus, whose extramarital affair with his 40-year-old biographer Paula Broadwell forced his sudden resignation last week, just three days after Obama's re-election.

Lawmakers from both parties, and from the Senate as well as the House of Representatives, have clamored for Petraeus and others to speak at various classified hearings to learn more about the circumstances of the attack.

Secretary of State Hillary Clinton has committed to testifying before the House and Senate Foreign Relations Committees once the State Department's Accountability Review Board report is concluded "by early-mid December," Ros-Lehtinen said Thursday. No date for Clinton's testimony was announced.

Obama has said he bears full responsibility for any failings connected to Benghazi and on Wednesday he slammed Republican lawmakers for criticizing US ambassador to the United Nations Susan Rice over her statements on the attack.

Republicans have zeroed in on the shifting narrative of the assault, which the administration initially said had stemmed from a spontaneous protest sparked by an offensive anti-Islam video posted on the Internet.

Rice delivered a version of that explanation on Sunday talk shows following the attack, but the administration later backtracked, admitting there had been no protest, but rather a coordinated assault by Islamist militants.

That has now led McCain and Graham to call for special "Watergate-style" hearings into the Benghazi attack and they have vowed to thwart the promotion of Rice to secretary of state in Obama's second term.

An angry Obama fired back, saying "to besmirch her reputation is outrageous" and that if he felt Rice was the best candidate he would go ahead and pick her to succeed Clinton when she steps down next year.

Graham, a hawkish Republican keen to prevent any primary challenge from his right in the 2014 mid-term elections, swiftly responded to Obama's remarks.

"Mr President, don't think for one minute I don't hold you ultimately responsible for Benghazi," Graham said in a statement. "I think you failed as commander in chief before, during, and after the attack."

McCain meanwhile said on the Senate floor Wednesday that the Obama administration "has either been guilty of colossal incompetence or engaged in a cover-up, neither of which are acceptable to the American people."

The battle carried on into the House hearing Thursday, where Republican Dana Rohrbacher complained there was no administration witness there "to explain under oath what the details of this debacle really are."

"The arrogance and dishonesty reflected in all of this is a little bit breathtaking, and it's about time that the president of the United States decides to level with the American people," he said.

Petraeus was CIA director at the time of the attack, in which two former Navy SEALs working for his agency were killed. He stepped down last week to pre-empt the revelation of his affair with Broadwell.

FBI agents uncovered his affair after Tampa socialite Jill Kelley complained of threatening emails they later traced back to Broadwell, who apparently viewed Kelley, a Petraeus family friend, as a competitor for his affections.

The probe also revealed thousands of emails exchanged between Kelley and General John Allen, Petraeus's successor as top commander in Afghanistan, including some described as "inappropriate" or "flirtatious."

Obama said on Wednesday that the scandal did not threaten national security, and officials have said there is no evidence that classified information was leaked by anyone involved in the investigation.