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Federal Reserve Governor Lisa Cook is refusing to resign after President Donald Trump said in a letter that he had removed her from her position “effective immediately.” The fight is raising questions about the president’s authority and the independence of the U.S. central bank.

Trump posted the letter on Truth Social to Cook on Thursday, five days after he first called on the Fed governor to resign on the social media platform. In the letter, Trump said that his actions were authorized by the U.S. Constitution and the Federal Reserve Act of 1913, which states that the president can remove governors from the Fed’s Board “for cause.” Trump said he believed there was “sufficient reason to suspect” that Cook “made false statements on one or more mortgage agreements.”

“I have determined that faithfully enacting the law requires your immediate removal from office,” Trump wrote.

Trump’s claims are based on a criminal referral by Bill Pulte, a Trump appointee to the agency that regulates Fannie Mae and Freddie Mac, who accused Cook of falsely claiming two primary residences to qualify for better mortgage rates. Pulte, who was Fox News’ Senior Advisor, went on Fox Business’ “Mornings with Maria” to discuss the allegations.

“It’s very odd to see people try to twist back way sideways and upside down to justify mortgage fraud,” Pulte said. “This is a very serious crime. Mortgage fraud carries up to 30 years in prison. I believe the president has ample cause to fire Lisa Cook. Whether he wants to do that or not is entirely up to the president. However, we will go where mortgage fraud is. If mortgage fraud is with a Republican or a Democrat, it doesn’t matter—if you commit mortgage fraud in President Trump’s America, we’re going to come after you. And Lisa Cook is no exception to that.”

Pulte filed the referral to the Justice Department on Aug. 15, alleging Cook falsified bank documents and property records. There have been no formal charges.

Cook was appointed to the Federal Reserve Board in 2022 by President Joe Biden. Cook told Fox News Digital she would not resign after Trump’s letter. “President Trump purported to fire me ‘for cause’ when no cause exists under the law, and he has no authority to do so. I will not resign. I will continue to carry out my duties to help the American economy as I have been doing since 2022,” Cook said.

Cook is being represented by Abbe Lowell, the high-profile attorney who has represented Hunter Biden, New York Attorney General Letitia James, Jared Kushner, and Ivanka Trump. Lowell told Fox News Digital about Trump’s letter. “President Trump has taken to social media to once again ‘fire by tweet,’ and once again his reflex to bully is flawed and his demands lack any proper process, basis, or legal authority. We will take whatever actions are needed to prevent his attempted illegal action,” Lowell said.

FOX Business has contacted the Federal Reserve for comment, but officials did not immediately respond.

Lowell then announced on Friday that he would be filing a lawsuit to formally challenge Trump’s move to fire Cook. “President Trump has no authority to remove Federal Reserve Governor Lisa Cook. His attempt to fire her, based solely on a referral letter, lacks any factual or legal basis. We will be filing a lawsuit challenging this illegal action,” he said.