Sen. Lindsey GrahamLindsey Olin GrahamTrump’s damage control falters Trump: 'I think I did great at the news conference' George Will calls Trump ‘sad, embarrassing wreck of a man’ MORE (R-S.C.) on Sunday said that former CIA Director David Petraeus, who resigned Friday, might still need to testify before Congress about the September attack on the U.S. Consulate in Benghazi, Libya.

Graham called Petraeus's testimony "essential" to understanding what happened in Libya during the attack. 

"I don't see how in the world you can find out what happened in Benghazi before, during, and after the attack if Gen. Petraeus doesn't testify," he said on CBS’s “Face the Nation.”

Petraeus resigned from the top post at the CIA on Friday after an extramarital affair with his biographer became public.

Graham also said that with a number of hearings and briefings by different committees scheduled in the next week, lawmakers should consider combining their efforts to investigate the deadly attack.

“I think that would be smart for the Congress to combine resources," said Graham.

Graham also said he would not vote to approve current U.S. Ambassador to the United Nations Susan Rice if she were nominated to replace Hillary ClintonHillary Diane Rodham ClintonState Dept: Russia’s allegations about American citizens ‘absolutely absurd’ Trump on possible sit-down with Mueller: 'I've always wanted to do an interview' Election Countdown: Senate, House Dems build cash advantage | 2020 Dems slam Trump over Putin presser | Trump has M in war chest | Republican blasts parents for donating to rival | Ocasio-Cortez, Sanders to campaign in Kansas MORE as secretary of State.

Graham said on he is “not entertaining promoting anybody who I think was involved in the Benghazi debacle.”

“There are too many questions to be answered. I do not personally trust her rendition of Benghazi,” he added.

The U.N. ambassador has faced sharp criticism for her handling of the attack in Benghazi, in particular her claim in the days after the attack that it was the result of a spontaneous anti-American protest sparked by anger over a film critical of Islam.

The administration later said the attack was a planned, terrorist assault. Obama officials, though, have defended the altered narrative, claiming it was based on the intelligence available at the time. 

"I think Susan Rice would have an incredibly difficult time to get through the Senate. I would not vote for her unless there's a tremendous opening up the information explaining herself in a way she has not yet done," Graham added.

"I'm not going to promote somebody who I think has misled the country or is either incompetent."