A divided federal appeals court on Monday refused to let President Donald J. Trump immediately oust Federal Reserve Governor Lisa D. Cook, but a forceful dissent warned that the decision misapplied both constitutional law and common sense.

In an order issued Monday night, the U.S. Court of Appeals for the District of Columbia Circuit denied the administration’s emergency request to lift a lower-court injunction that had restored Ms. Cook to her post after Mr. Trump declared he had “cause” to remove her. Judge Bradley Garcia, joined by Judge J. Michelle Childs, filed a concurring opinion. Judge Gregory Katsas dissented.

The Federal Reserve is scheduled to begin a two-day meeting of the Federal Open Market Committee on Tuesday. Monday’s order likely means that Cook will be able to attend t

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