WASHINGTON -- Sen. Lindsey Graham threatened Tuesday to block Senate consideration of President Barack Obama’s nominee to head the CIA in retaliation for the Obama administration’s failure to provide more details about the Sept. 11 attack on the U.S. consulate in Benghazi, Libya.

The South Carolina Republican’s threat to place a hold on the nomination of John Brennan as CIA director raises doubts about a second senior national security leadership pick by Obama, with several senators already questioning former Sen. Chuck Hagel’s qualifications to be defense secretary.

Graham, a Senate Armed Services Committee member who served as a military lawyer in Iraq and Afghanistan, also voiced concerns about Hagel, a former Republican senator from Nebraska who was nominated Monday. But Graham indicated likely support for Obama’s pick of Sen. John Kerry, a Massachusetts Democrat, to be secretary of state.

Criticism over the Benghazi assault, which killed four Americans, from Graham and fellow Republican Sens. John McCain of Arizona and Kelly Ayotte of New Hampshire contributed to U.N. Ambassador Susan Rice’s decision last month to withdraw her name for consideration as secretary of state.

Graham brought up Rice again Tuesday in explaining why he is weighing a block of Brennan’s nomination to head the CIA.

“I have not forgotten about the Benghazi debacle and still have many questions about what transpired before, during and after the attack on our consulate,” Graham said in a prepared statement.

“In that regard, I do not believe we should confirm anyone as director of the CIA until our questions are answered – like who changed Ambassador Susan Rice’s talking points and who deleted the references to al Qaida?” Graham said. “My support for a delay in confirmation is not directed at Mr. Brennan, but is an unfortunate, yet necessary action to get information from this administration.”

In appearances on TV talk shows Sept. 16, five days after the Benghazi attack, Rice described them as spontaneous violent responses to an anti-Islam film produced in the United States.

Her description contradicted subsequent claims by the CIA and other senior U.S. officials who said the attack was well-planned and coordinated by al Qaida terrorists.

Rice and her defenders later said she had relied in her initial account on talking points provided to her by the White House, but Senate investigators subsequently found that several intelligence agencies had changed them to remove references to al Qaida participation in the Benghazi assault.

White House Press Secretary Jay Carney on Tuesday criticized Graham for threatening to delay Brennan’s nomination.

“It would be unfortunate, I think, if in pursuit of this issue, which was highly politicized, the Senate would hold up the nomination of John Brennan to be director of the Central Intelligence Agency,” Carney told reporters. “As the president said yesterday, that post, as well as the position of secretary of defense, secretary of state – these are essential positions that need to be filled, if possible, without delay.”

Obama chose Brennan, who has held several senior counterterrorism posts under Obama and President George W. Bush, to replace David Petraeus after the retired general resigned after acknowledging an extramarital affair.

Carney blamed the changes in Rice’s talking points on “the process . . . of declassifying classified information,” and he ridiculed “the continued political fascination with appearances on Sunday (news) shows.”

Graham, however, said it may have been Obama aides who politicized the issue in the run-up to the Nov. 6 election.

“It is imperative we understand who changed the talking points just weeks before a presidential election, and why,” Graham said. “The stonewalling on Benghazi by the Obama administration must come to an end.”

Appearing on a radio show in South Carolina, Graham contrasted his opposition to Hagel with his likely support for Kerry, both of whom he served with in the Senate.

“Chuck Hagel’s positions on Iran and Israel are dangerously out of the mainstream,” Graham said. “He was one of 12 senators who refused to sign a letter to the European Union asking that Hezbollah be designated a terrorist organization. He asked that Israel negotiate directly with Hamas. And he was one of two senators who voted against sanctions against Iran, saying we should have direct negotiations.”

By contrast, Kerry, the 2004 Democratic presidential nominee, “has been Foreign Relations (Committee) chairman for years; he’s pretty good on Syria; he’s certainly qualified; his views are in the mainstream,” Graham said.

Lesley Clark and Jonathan S. Landay contributed to this report