WASHINGTON — President Donald Trump fired Federal Reserve Governor Lisa Cook late Monday, a surprise move constituting a sharp escalation in his battle to exert greater control over what has long been considered an institution independent from day-to-day politics.

Trump said in a letter posted on his Truth Social platform that he is removing Ms. Cook because of allegations that she committed mortgage fraud. Bill Pulte, a Trump appointee to the agency that regulates mortgage giants Fannie Mae and Freddie Mac, made the accusations last week.

Mr. Pulte alleged that Ms. Cook had claimed two primary residences — in Ann Arbor, Mich., and Atlanta — in 2021 to get better mortgage terms. Mortgage rates are often higher on second homes or those purchased to rent.

The announcement came days after

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