By Elisabeth Buchwald, Bryan Mena, CNN

(CNN) — President Donald Trump on Monday said he has fired Federal Reserve Governor Lisa Cook, according to a letter addressed to her posted on his social media — the first instance of a president firing a central bank governor in the central bank’s 111-year history.

The unprecedented move represents a significant escalation of the president’s battle against the Fed, which he has blamed for taking too long to lower interest rates. But Cook said the president doesn’t have the “authority” to fire her and that she plans to continue in her post.

Cook has recently come under fire by Trump and members of his administration for allegedly committing mortgage fraud. The Justice Department has said it plans to investigate those allegations first raised by Federal Housing Finance Director Bill Pulte.

Cook has not been charged with any wrongdoing.

“President Trump purported to fire me ‘for cause’ when no cause exists under the law, and he has no authority to do so,” Cook said in statement her attorneys shared with CNN Monday night. “I will not resign. I will continue to carry out my duties to help the American economy as I have been doing since 2022.”

The Fed declined to comment on the news.

It’s unclear whether Trump has the legal authority to fire Cook over these allegations. The law specifies that a president may only remove members of the Fed’s board “for cause” – though what merits a for-cause firing has not been explicity defined.

Trump, in his letter to Cook wrote, “I have determined that there is sufficient cause to remove you from your position.”

(A CNN review of mortgage documents shows that Cook took out mortgages for two properties, both of which were listed as her principal residence. However, it’s not known why she did so or if she did so intentionally.)

“In light of your deceitful and potentially criminal conduct in a financial matter … I do not have such confidence in your integrity. At a minimum, the conduct at issue exhibits the sort of gross negligence in financial transactions that calls into question your competence and trustworthiness as a financial regulator,” Trump added in his letter.

“This is not DOJ opening anything, they haven’t charged her. So as of right now, I think it’s kind of questionable for cause,” former Federal prosecutor Shan Wu told CNN’s Brianna Keilar, referring to the Department of Justice. “It’s definitely gonna get litigated.”

Appointed to the Fed board by former President Joe Biden in 2022, Cook is the first Black woman to serve as a Fed governor.

While the firing may be challenged in courts, even going up to the Supreme Court, Trump’s firing of Cook puts the central bank of the world’s largest economy in uncharted waters.

For example, it’s unknown whether Cook would have to leave the Fed’s board immediately, and if so, will Trump have the opportunity to nominate someone else to fill her seat. Cook’s attorney, Abbe David Lowell of Lowell & Associates, said in a statement to CNN: “We will take whatever actions are needed to prevent his attempted illegal action.”

The Fed’s next monetary policy meeting is less than a month away, over September 16 and 17.

Last week Cook released a statement saying she would not be “bullied” into resigning.

“I have no intention of being bullied to step down from my position because of some questions raised in a tweet. 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,” she said in that statement.

Fed independence at risk

The Fed is designed to be independent from politicians specifically so it can focus on economic data – and not political considerations – in achieving its dual mandate to keep price increases in check while supporting the job market.

Politicians often prefer lower interest rates, aiming to boost stock prices and make it cheaper for people to borrow money, both popular moves among voters. But lower interest rates risk igniting price pressures. On the other hand, leaving rates too high could overly restrict spending and hiring, hurting the economy.

No central bank gets it right all the time. However, studies strongly suggest that economies with independent central banks experience better outcomes, including lower inflation.

If the move costs the US its economic credibility, American assets, such as stocks and the dollar, could get hammered. That in turn could leave investors to demand higher premiums to lend money to the US.

“The bigger picture is sadly simple: The Fed is designed to be independent of politics, for very good reasons,” Alan Blinder, a former vice chair at the Fed told CNN Monday night. “He is trying to end that and make it an arm of the Trump administration, which will be very bad for monetary policy if it happens.”

Senator Elizabeth Warren, the top-ranking Democrat on the Senate Banking Committee, said in a statement that Trump’s attempt to fire Cook is “an authoritarian power grab that blatantly violates the Federal Reserve Act, and must be overturned in court.”

Representatives for Republican Senator Tim Scott, who leads the committee, did not immediately respond to CNN’s request for a comment.

Immediately following Trump’s announcement on Monday, the US dollar index dropped by 0.3%. The index measures the strength of the dollar against a basket of international currencies.

US stock futures, meanwhile, slid further after a day in the green. Dow futures fell 100 points, or 0.2%. S&P 500 futures fell 0.3%. Nasdaq 100 futures slipped 0.5%.

The price of gold, which is considered a safe haven asset during times of uncertainty, rose 0.45%.

This story has been updated with additional context and developments.

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CNN’s Matt Egan, John Liu and John Towfighi contributed reporting.