Just-resigned CIA Director David Petraeus says he will testify this week at congressional hearings looking into the attack on the U.S. consulate in Benghazi, Libya, as new details emerge about the emails that helped end his career. NBC's Andrea Mitchell reports.

Updated at 4:44 p.m. ET: President Barack Obama on Wednesday spiritedly defended U.N. Ambassador Susan Rice over her response to the September attack on the U.S. mission in Benghazi, Libya, that left four Americans dead, assailing Republican criticism of her as "outrageous."

At his first news conference since winning re-election, the president said Rice has done “exemplary work” and accused GOP critics of trying to “besmirch” her reputation.

President Obama defends U.N. ambassador Susan Rice against criticism from Sen. John McCain and Sen. Lindsey Graham over the Benghazi attacks in Libya.

“I don’t think there’s any debate in this country that when you have four Americans killed, that’s a problem, and we’ve got to get to the bottom of it and there needs to be accountability. We’ve got to bring those who carried it out to justice. They won’t get any debate from me on that,” Obama said sternly.

“But when they go after the U.N. ambassador, apparently because they think she’s an easy target, then they’ve got a problem with me.”

Two of Rice’s main GOP critics refused to back down.

Sen. John McCain (R-Ariz.) discusses the Obama administration's handling of the aftermath of the Benghazi attack, accusing the president of "either a cover-up or incompetence." McCain also vowed to block any nomination of UN Ambassador Susan Rice for secretary of state to replace Hillary Clinton.

Sen. Lindsey Graham said shortly after Obama’s news conference that he had “no intention of promoting anyone who is up to their eyeballs in the Benghazi debacle.” Sen. John McCain added: "We owe the American people and the families of the murdered Americans a full and complete explanation, which for two months the President has failed to deliver.”

Bebeto Matthews / AP file U.S. Ambassador Susan Rice speaks during a meeting on Syria in the United Nations Security Council, Aug. 30.

Rice has been mentioned as a possible successor to U.S. Secretary of State Hillary Clinton, who has said she will not continue to serve in Obama's second term beginning in January.

Senior Republican senators vowed earlier on Wednesday to block any future promotion of Rice, questioning her initial description of the Sept. 11 violence on the U.S. consulate in Benghazi as a spontaneous outburst rather than a planned attack as unfathomable. Killed in the violence were U.S. Ambassador Chris Stevens and three other American officials.

“My judgment at this time is that four Americans were killed, and the information that our U.N. ambassador conveyed was clearly false," McCain, R-Ariz., the top GOP senator on the Armed Services Committee, told reporters at a Capitol Hill news conference. "There was overwhelming evidence that it was completely false. And she should have known what the situation and circumstances were and not tell the world on all Sunday morning talk shows.”

Graham, of South Carolina, supported that stance at the same news conference, saying of Rice, "I don't trust her. And the reason I don't trust her is because I think she knew better, and if she didn't know better, she shouldn't be the voice of America.”

The two lawmakers along with Sen. Kelly Ayotte of New Hampshire are pressing for a special, Watergate-style select Senate committee to investigate the Benghazi attack. They complained that separate inquiries by various Senate panels will fail to get to the bottom of the deadly incident.

Sen. John McCain took to the Senate floor to protest the potential appointment of U.N. Ambassador Susan Rice. At issue are Rice's comments that Benghazi was triggered by a video maligning the Prophet Mohammad. NBC's Kelly O'Donnell reports.

Rice has been the focal point of accusations that the Obama administration misled the public about the nature of the Benghazi attack. Five days after the attack, she appeared on several news talk programs and said the attack stemmed from outrage in the Arab world over an anti-Muslim video, not an act of terrorism. The White House later corrected that claim.

Obama wouldn’t comment on whether he’d nominate Rice to replace Clinton on his Cabinet. But he said of Rice: “She has done exemplary work.”

“She made an appearance at the request of the White House in which she gave her best understanding of the intelligence (on Benghazi) that had been provided to her. If Sen. McCain and Sen. Graham and others want to go after somebody, they should go after me – and I’m happy to have that discussion with them," he said animatedly.

“But for them to go after the U.N. ambassador, who had nothing to do with Benghazi and was simply making a presentation based on intelligence that she had received, and to besmirch her reputation, is outrageous.”

Shortly after the president’s remarks, Graham issued the following statement:

“Mr. President, don’t think for one minute I don’t hold you ultimately responsible for Benghazi. I think you failed as Commander in Chief before, during, and after the attack. We owe it to the American people and the victims of this attack to have full, fair hearings and accountability be assigned where appropriate. Given what I know now, I have no intention of promoting anyone who is up to their eyeballs in the Benghazi debacle.”

McCain said initial Obama administration statements the the Benghazi attack was triggered by a spontaneous demonstration and a hateful video “clearly did not comport with the facts on the ground.“

In a statement issued after Obama’s news conference, McCain repeated his call for a select committee to be appointed “to obtain a full and complete accounting which would be credible with the American people."

Not all Republican senators agree with the the need for a special select committee.

Sen. Susan Collins, R-Maine, said she did not “see the benefit” of such an approach, noting the Homeland Security Committee has governmentwide jurisdiction and “a history of producing comprehensive bipartisan reports.”

Sen. Joe Lieberman, I-Conn, said assigning the matter to a select committee at this point would be “premature.”

David Petraeus, who stepped down as CIA director last week after acknowledging an extramarital affair, has agreed to testify before Congress on the Benghazi attack. He'll go before the Senate Intelligence Committee on Thursday and the House committee on Friday.

Rep. Dutch Ruppersberger, D-Md., the ranking member on the House Intelligence Committee, said Wednesday that he would like to hear from Petraeus but has yet to formally request a meeting with him.

NBC News Capitol Hill Correspondent Kelly O’Donnell and NBC News Associate Producer Catherine Chomiak contributed to this report.

More from the news conference:

President Barack Obama holds his first press conference at the White House since being re-elected to a second term.

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