WASHINGTON — For President Obama, the decision to forgo the fight to make Susan E. Rice his secretary of state was a deeply painful one. It required publicly abandoning one of his most loyal aides, who had broken with the Democratic foreign policy establishment early to side with his improbable candidacy, and whose blunt-speaking style — which helped cost her the job — had always been, for Mr. Obama, a part of her appeal.

Typically, just hours before she called Mr. Obama to tell him she had decided to withdraw from contention as Hillary Rodham Clinton’s successor, she rebuked her Chinese counterpart in an informal meeting of the United Nations Security Council, telling him his views excusing a North Korean missile launching this week were “ridiculous.”

He shot back, according to witnesses, that she “better watch your language.”

It was the latest example of why Ms. Rice, the American ambassador to the United Nations, has so often been criticized as being an unusually undiplomatic diplomat, direct to the point of rudeness. But friends and former White House aides say that Ms. Rice’s style is a reflection of Mr. Obama’s own: impatient with niceties, uninterested in small talk or long dinners, focused solely on results.

“They share a common vision and a common style,” said Madeleine Albright, the former secretary of state, who has known Ms. Rice since she was 4 years old and a schoolmate of Ms. Albright’s children. “Some of it is a generational thing, and some of it is life’s experiences.”