Federal Reserve governor Lisa Cook late Wednesday said she would not leave her post after Trump on social media called on her to resign over an accusation from one his officials that she committed mortgage fraud.

“I have no intention of being bullied to step down from my position because of some questions raised in a tweet,” Cook said in a statement issued by the Fed.

Bill Pulte, the head of the agency that regulates mortgage giants Fannie Mae and Freddie Mac and a Trump appointee, alleged on the X social media platform early Wednesday that Cook had claimed two primary residences -- in Ann Arbor, Michigan and Atlanta -- in 2021 to get better mortgage terms. Mortgage rates are often higher on second homes or those purchased to rent.

Trump followed up Pulte's accusation by calling on Cook to resign, in the latest effort by the administration to exert greater control over one of the few remaining independent agencies in Washington. Trump has repeatedly attacked the Fed's chair, Jerome Powell, for not cutting its short-term interest rate, and even threatened to fire him.

If Cook is forced off the Fed's governing board, it would provide Trump an opportunity to appoint a loyalist. Trump has said he would only appoint officials who would support cutting rates.

Pulte urged the Justice Department to investigate Cook, who was appointed to the Fed’s governing board by former president Joe Biden in 2022. She was reappointed the following year to a term that lasts until 2038, the longest remaining term among the seven governors.

Cook also said, “I do intend to take any questions about my financial history seriously as a member of the Federal Reserve and so I am gathering the accurate information to answer any legitimate questions and provide the facts.”

Pulte, in a letter to Attorney General Pam Bondi, said that on June 18, 2021, Cook purchased a home in Ann Arbor and then two weeks later bought a condo in Atlanta. Before joining the Fed, Cook taught at Michigan State University. Pulte also charged that Cook has listed her condo in Atlanta for rent.

A Justice Department spokesperson declined to comment.