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US President Obama has lambasted top Republicans for attacking the diplomat tipped as a possible replacement for Secretary of State Hillary Clinton.
Republicans said UN Ambassador Susan Rice should not be promoted, citing her response to September's deadly attack on the US consulate in Libya.
Mr Obama said the attacks on Ms Rice were "outrageous" and challenged her critics to "go after me" instead.
Republicans called for a committee to investigate the Libya attack.
In the wake of the 11 September assault on the US mission in Benghazi, Ms Rice framed it as a spontaneous protest over an anti-Islamic film made in the US.'Cover-up'
The Obama administration later blamed the attack on al-Qaeda-linked militants, adding that the earlier account was based on the best information available at the time.
Sen John McCain vowed on Wednesday to block any move to appoint Ms Rice to replace Mrs Clinton as America's top diplomat.
He introduced a Senate resolution calling for the establishment of a special committee to investigate the Benghazi attack, which left four Americans dead, including the US ambassador.
"This administration has either been guilty of colossal incompetence or engaged in a cover-up," he said on the Senate floor.
Lindsey Graham, another Republican senator, said he did not trust Ms Rice and called for "Watergate-style" hearings into the Libya incident.
In his first White House news conference since last week's election, President Obama said: "If Senator McCain and Senator Graham and others want to go after somebody, they should go after me.
"But when they go after the UN ambassador, apparently because they think she's an easy target, then they've got a problem with me."
"To besmirch her reputation, is outrageous," he added.Nomination showdown
Shortly after Mr Obama's remarks, Sen Graham showed no sign of backing down.
"Mr President, don't think for one minute I don't hold you ultimately responsible for Benghazi," he said in a statement.
"I think you failed as commander in chief before, during and after the attack."
Mr Obama would not be drawn during Wednesday's news conference on possible cabinet appointments.
But the president insisted he would nominate Ms Rice if she was the best choice to lead the Department of State. Mrs Clinton plans to return to private life.
Wednesday's political showdown raised the prospect of a prolonged nomination for Ms Rice, who would be the second female African-American secretary of state, if she is picked by Mr Obama.
Another name mentioned for the post is Senate Foreign Relations Committee Chairman John Kerry, a Democrat, who would be expected to breeze through a Capitol Hill confirmation hearing.
But picking Sen Kerry would create another headache for Mr Obama's Democrats - fending off a Republican challenge for his open Senate seat in Massachusetts.
During his news conference, Mr Obama also said he was not aware of any leak of classified information by former CIA Director David Petraeus, who quit last Friday because of an extramarital affair.
The House Permanent Select Committee on Intelligence said Gen Petraeus would testify about the Benghazi attack in a closed-door hearing on Friday