Republicans toned down criticism of U.N. Ambassador Susan E. Rice on Sunday, shifting the focus of their inquiries into the Sept. 11 attack on the U.S. Consulate in Benghazi, Libya, to the State Department’s inaction on security requests in the days leading up to the terrorist assault and the Obama administration’s handling of the aftermath.

Two departing Republican senators, Jon Kyl of Arizona and Kay Bailey Hutchison of Texas, said they have concerns about a White House “cover-up” about the incident, which left four Americans dead.

“There are three questions that have to be answered,” Mr. Kyl said in an interview broadcast Sunday on CNN’s “State of the Union.” “Why weren’t the warnings about the need for security heeded? Why weren’t the requests for help during the attack answered? And why did the administration think it had to cover up all the things that occurred before by putting out to the American people a narrative that I think will turn out to be absolutely false?”

Mrs. Hutchison, appearing on the same program, echoed his comments: “On Sept. 20, the Senate was given a classified briefing, and they were still, the top-level people were still telling us the same thing. They were telling us things that we knew, that we even saw in the press, were not correct.”

Republicans, led by Sen. John McCain of Arizona, have turned up the heat on President Obama by convening hearings in the House and Senate and assailing the White House for unexplained delays in declaring the assault a terrorist attack with links to al Qaeda.

Until last week, Republican lawmakers — along with some Democrats — focused their questions on Mrs. Rice, who made several high-profile news show appearances on Sept. 16 blaming the attacks on reaction to an anti-Islam YouTube video.

Mr. McCain previously said Mrs. Rice’s discredited comments should disqualify her as one of Mr. Obama’s candidates to replace outgoing Secretary of State Hillary Rodham Clinton. On Sunday, the Arizona Republican, who ran for the White House against Mr. Obama in 2008 and has been one of his sharpest critics on Capitol Hill, softened his opposition to the U.N. ambassador.

In an appearance on “Fox News Sunday,” Mr. McCain said Mrs. Rice should have a chance to defend herself.

“I’d be glad to have the opportunity to discuss these issues with her,” Mr. McCain said. But she has to explain, he said, why she asserted that “al Qaeda has been decimated in her statement They’re on the rise in the Middle East.”

Rep. Peter T. King, chairman of the House Homeland Security Committee, said Mrs. Rice has done a good job at the United Nations, but, like Mr. McCain, the New York Republican said he wants answers about Benghazi.

“If she is sent out to speak to the American people on what happened in Benghazi, she is obligated to do more than look at three sentences of unclassified or five sentences of unclassified talking points,” Mr. King said on NBC’s “Meet the Press.” “She has an obligation not to just be a puppet and take what’s handed to her.”

Sen. Lindsey Graham, who with Mr. McCain has been leading the anti-Rice chorus in Congress, also seemed to backtrack Sunday.

“This is about four dead Americans. This is about a national security failure,” said Mr. Graham, South Carolina Republican. “I blame the president above all others.”

Mr. Graham, who vowed this month to block a potential Rice nomination to head the State Department, said Sunday that “when she comes over, if she does, there will be a lot of questions asked of her about this event and others.”

Mr. Obama pushed back sharply against Republican criticism of Mrs. Rice in his first postelection news conference on Nov. 14 by saying Mr. McCain and Mr. Graham should “go after me,” not the ambassador.

Since then, Democrats, especially members of the Congressional Black Caucus, have rallied around the 48-year-old Stanford graduate, the nation’s first black woman to serve as ambassador to the United Nations. Rep. Marcia Fudge, Ohio Democrat and incoming chairwoman of the caucus, said Nov. 16, “It is a shame that anytime something goes wrong, they pick on women and minorities.”

But race has nothing to do with the frustration over Benghazi, Mr. Graham said last week: “When you can’t answer the question, you attack the questioner. The only color I’m worried about when it comes to Benghazi is red — blood red, the death of four Americans.”

Sen. Joe Lieberman, Connecticut independent, said if the president wants to nominate Mrs. Rice to the secretary of state post, the truth about the Benghazi attacks has to come out.

“In fairness to Ambassador Rice, there ought to be the widest public airing of what led to her statements and others in the administration, particularly, obviously, if she’s going to be nominated for secretary of state or some other high office,” he said in a CNN interview aired Sunday. “She’s had a distinguished career up until now.”

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