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“I want to make sure is that Iran is actually not hopeful, but they are fearful as a result of our nominee for secretary of defense,” she said on “Fox News Sunday.”

Sen. John McCain, Arizona Republican, who served with Mr. Hagel on the Senate Foreign Relations Committee and considers the nominee a friend, said he will wait until the former senator appears at his nomination hearings before deciding whether he will support his bid.

“My questions about him are: What is his view of America’s role in the world?” Mr. McCain said.

Mr. Powell said critics who question the nominee’s willingness to project American military might around the world should remember who won the presidential election.

“I’m still a Republican,” Mr. Powell said, but “it’s ‘President Obama.’ Not ‘President McCain’ and not ‘President [Mitt] Romney.’ [Republicans] have lost two elections. The American people have made it clear that they are not particularly interested in finding new conflicts to get into.”

Many Republican troubles can be traced to the party’s contentious relationship with minority voters, said the retired four-star Army general and the nation’s first black secretary of state.

“There’s a dark vein of intolerance in some parts of the party,” he said, citing what he contends were racially tinged comments about Mr. Obama last fall from former Alaska Gov. Sarah Palin and former New Hampshire Gov. John H. Sununu.

Mrs. Palin in October described Mr. Obama’s handling of the terrorist attack in Benghazi, Libya, as a “shuck-and-jive shtick,” and Mr. Sununu raised eyebrows the same month when he described the president’s poor first debate performance as “lazy.”