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Mr. Duncan and Mr. Obama, both of whom advocate public charter schools, have been outspoken in recent days about the state of education in general and D.C. schools in particular.

On Sunday, Mr. Duncan and Ms. Rhee appeared on NBC’s “Meet the Press,” where he said U.S. education reform has a “long, long” way to go.

He also praised Ms. Rhee’s reforms and said he is a “huge fan.” And he has recommended that she be retained as schools chief.

His comments led an elected D.C. school official to say on Monday that Mr. Duncan should “butt out” of local school affairs.

Asked for reaction to that comment Wednesday, Mr. Duncan’s press secretary, Justin Hamilton, said, “We’ll let the secretary’s comments speak for themselves.”

Mr. Obama appeared Monday on “The Today Show,” where, when asked by a viewer whether he would send daughters Malia and Sasha to a D.C. public school, he said, “The answer is ‘no,’ right now.

“The D.C. public school systems are struggling,” though “they have made some important strides over the last several years to move in the right direction of reform.”