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Mr. Hagel also has been criticized by gay groups, liberal and conservative, for his 1998 opposition to a U.S. ambassador as “openly, aggressively gay.” While Mr. Hagel has apologized for the comments and no current Democratic lawmaker has called them disqualifying, The Washington Post and former Democratic Rep. Barney Frank of Massachusetts have said Mr. Hagel should not be confirmed.

“The administration has a lot of work to do on Hagel,” a Democratic Senate aide acknowledged to Reuters news agency Sunday.

In an appearance on ABC’s “This Week,” Senate Minority Leader Mitch McConnell, Kentucky Republican, said Mr. Hagel will get a fair confirmation hearing if he is nominated, but Mr. McConnell said the 66-year-old will have to explain his controversial comments.

“I’m going to take a look at all of the things Chuck has said over the years and review that, and in term of his qualifications to lead our nation’s military,” Mr. McConnell said. “He certainly has been outspoken on foreign policy and defense over the years. The question we will be answering if he is the nominee is: Do his views make sense for that particular job?”

Mr. Hagel, who retired from the Senate in 2009, became estranged from many in his party after he became a fierce critic of President Bush and the Iraq War in 2005.

He also has irked conservatives and pro-Israel groups with his advocacy of direct talks with the Islamic extremists who rule Iran and with his calls for a more conciliatory approach to anti-Israel groups such as Hezbollah.

By his last year in the Senate, Mr. Hagel had become a de facto Democrat. He traveled with Mr. Obama to Iraq during his presidential campaign. On returning to Washington, he defended the Democratic candidate and criticized the Republican nominee, Sen. John McCain of Arizona.

Since leaving office, Mr. Hagel has endorsed Democrats running for the Senate, and many Democrats and others on the left have rallied to his defense.

Lawrence J. Korb, a military analyst at the liberal Center for American Progress think tank, run by former Bill Clinton aide John Podesta, said it would be a mistake for Mr. Obama to back off Mr. Hagel after yielding on Mrs. Rice.

Mr. Korb, who served as assistant defense secretary in the Reagan administration, said, “I’ve never seen a person more qualified than Hagel. … Here’s a person who has been a legislator. He knows foreign policy. He’s done well in the private sector. And he’s a war hero.”

He added, “Most people feel if Obama backs off again, that’s going to send the wrong signal.”

Mr. Hagel served in the Senate from 1996 to 2009, and most recently as co-chairman of Mr. Obama’s Intelligence Advisory Board since 2009. He is also a professor at Georgetown University and chairman of the Atlantic Council.

A Vietnam War veteran, he was awarded two Purple Hearts.

If confirmed, Mr. Hagel will lead a Pentagon in transition — a department facing budget cuts and personnel reductions over the next decade, the withdrawal of troops from Afghanistan, and a shift from fighting large ground wars to focusing on building air and sea capabilities in the Persian Gulf and Asia-Pacific regions.