Updated

Republican Sen. Lindsey Graham suggested Sunday that he would try to hold up the appointment of President Obama’s nominees to run the CIA and the Defense Department until the White House provides more details about what the president and other top administration officials were doing the night of the Benghazi terror attacks.

The South Carolina senator is among congressional Republicans most critical of Defense Department nominee Chuck Hagel and the White House’s handling of the Sept. 11, 2012, attacks on a U.S. outpost in Benghazi, Libya. The attacks killed Ambassador Christopher Stevens and three other Americans.

“I don’t think we should allow … Hagel to be confirmed secretary of Defense until the White House gives us an accounting,” Graham said on CBS’ “Face the Nation.” “Did the White House ever pick up the phone and call anyone in the Libyan government to help these folks?”

Graham said he would do the same with the Senate confirmation hearing for John Brennan, the president’s chief counterterrorism adviser, to run the CIA.

“No confirmation without information,” he said.

Though Graham has not threatened to filibuster the Hagel nomination in the Democrat-controlled chamber, he has tried several other aggressive-but-less-drastic moves. He has called on Obama to withdraw the nomination and has successfully demanded that outgoing Defense Secretary Leon Panetta testify on Benghazi before a vote on Hagel.

On Sunday, Oklahoma Republican Sen. James Inhofe threatened on Fox News to filibuster the Hagel nomination, in an effort to make Hagel get 60 votes, note just the 51 majority, to be confirmed.

Democrats support the president’s nomination, but Republicans appear largely opposed to voting for Hagel, a former Nebraska Republican senator, largely over concerns about his support of Israel and whether he would back U.S. military action to stop Iran from producing a nuclear weapon.

Graham began making his case last week for more details about the White House response on the night of the attacks.

He vowed Friday to hold Obama "accountable" for his leadership during the incident, following Panetta and Joint Chiefs Chairman Gen. Martin Dempsey’s Senate testimony a day earlier.

Panetta and Dempsey testified that they had just one phone conversation with Obama on the day of the attacks that started at about 5 p.m. ET and lasted for about 30 minutes, which prompted Graham to ask why no follow-up calls took place.

Graham said Thursday on Fox News that the White House has so far “delayed, denied, deceived and stonewalled. And this has to come to an end. (Obama) has to account for his leadership."

He said Sunday that another remaining question is whether the president pressed the Libyan government to let a response team purportedly deployed from Tripoli to leave a Libyan airport to get to the U.S. outpost, which was under attack for about eight hours.

“We know nothing about what the president did during the night of Sept. 11 during a night of national crisis,” Graham said.

Rhode Island Democratic Sen. Jack Reed also appeared on the show and called Graham’s actions “unprecedented.” He also said Graham dwelling on the tragedy to block nominations was “not appropriate.”