President Donald Trump on Monday said he had fired Federal Reserve Board Governor Lisa Cook, an unprecedented and dramatic escalation of his attacks on the U.S. central bank's independence over its refusal to cut interest rates.

Trump, in a termination letter to Cook posted on Truth Social, cited allegations by Federal Housing Finance Agency Director Bill Pulte that she had made false statements on applications for home mortgages.

The letter came four days after the Department of Justice said it would investigate Cook because of Pulte's claim.

Cook, in a statement Monday, said, "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," said Cook, who is the first Black woman to serve as a Fed governor. "I will continue to carry out my duties to help the American economy as I have been doing since 2022."

Cook, who was appointed by former President Joe Biden, has hired the high-profile attorney Abbe Lowell to represent her. She has not been charged with any crime.

Lowell, in a statement, said, "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.

A spokesman for the Federal Reserve had no immediate comment on Trump's letter.

Trump's removal of Cook could be challenged in federal court. The Supreme Court could eventually rule on whether her firing is legal.

If it is upheld, Trump would be on track to have a Fed board whose majority is comprised of governors who he has appointed.

Congress curbed the president's authority to unilaterally fire a Fed governor in the Federal Reserve Act of 1913, which states that the president can only do so "for cause."

While the law does not elaborate on what constitutes "cause," it has historically been understood to mean malfeasance or dereliction of duty.

Trump, in his letter to Cook on Monday, tied Pulte's allegations about mortgage fraud to the public's perception of her actions as Fed governor.

The president wrote, "There is sufficient reason to believe you have made false statements on one or more mortgage agreements."

"For example, as detailed in the Criminal Referral, you signed one document attesting that a property in Michigan would be your primary residence for the next year," Trump wrote.

"Two weeks later, you signed another document for a property in Georgia stating that it would be your primary residence for the next year," he continued.

Trump claimed that it is "inconceivable" that Cook was "not aware of [her] first commitment when making the second."

"In light of your deceitful and potentially criminal conduct in a financial matter, [the American people] cannot and I do not have such confidence in your integrity," Trump wrote.

"At a minimum, the conduct that issue exhibits the sort of gross negligence in financial transactions that calls into question your competence and trustworthiness as a financial regulator."

Sen. Elizabeth Warren, D-Mass., in a statement on Monday night, said, "The illegal attempt to fire Lisa Cook is the latest example of a desperate President searching for a scapegoat to cover for his own failure to lower costs for Americans."

"It's an authoritarian power grab that blatantly violates the Federal Reserve Act, and must be overturned in court," said Warren, who is the ranking member of the Senate Banking, Housing, and Urban Affairs Committee.

Edward Mills, managing director of the financial advisory firm Raymond James, said that Trump's move to fire Cook "marks an unprecedented moment for both central bank independence, signaling the White House's escalating campaign to exert direct influence over monetary policy decisions."

"Markets are likely to view this attack on Fed independence negatively, amplifying uncertainty over future policy direction," Mills said.

Pulte applauded Trump's move and thanked his "commitment to stopping mortgage fraud and following the law" in a post on X.

Cook's termination comes after months of complaints by Trump about the Federal Reserve and its chairman, Jerome Powell, for not cutting interest rates as the president has demanded they do since he returned to the White House in January.

On July 15, Trump asked a group of Republican members of Congress if he should fire Powell, and they agreed he should, according to a senior White House official. Trump said he would follow through on that.

But a day later, Trump publicly denied that he would fire Powell even as he left the door open for it to happen at some point.

"We're not planning on doing it," he said at the time.

"I don't rule out anything he said. "But I think it's highly unlikely, unless he has to leave for fraud."

If Trump is ultimately successful in removing Cook, he will be able to nominate her replacement and reshape the Fed's governing board for the next several years. Fed governors typically serve 14-year terms.

Two of the seven current Fed governors, Christopher Waller and Michelle Bowman, are Trump appointees. Trump nominated Powell to be the Chair of the Federal Reserve in 2017.

As of Monday afternoon, there were six members on the Board of Directors, including Cook, with one seat vacant after the resignation of Adriana Kugler earlier this month.

Trump has nominated Stephen Miran, chair of the Council of Economic Advisors, to fill Kugler's seat.

If Miran is confirmed by the Senate and if Trump succeeds in removing Cook and getting her replacement confirmed, it would give Trump a 4-to-3 majority of appointees on the board.

The board, along with five regional presidents who are seated on a rotating basis, makes up the Federal Open Market Committee, which sets the central bank's key interest rate.

However, the board alone controls several other rates, including the interest paid on reserves that banks keep at the Fed.

After resisting pressure from Trump for months to cut rates, Powell last week suggested that conditions "may warrant" interest rate cuts as the Fed proceeds "carefully."

The ICE U.S. Dollar index, which measures the greenback against a basket of major currencies, shed 0.3% in a rapid move overnight just after Trump said he had fired Cook.

The 2-year Treasury yield, a rate sensitive to Fed moves, ticked lower by 4 basis points on the move. One basis point equals 0.01%.

Stock futures were lower in overnight trading before Trump's announcement and continued to slightly move lower after it.

Gold futures were the biggest mover other than the dollar, gaining 0.3%.

— CNBC's Jeff Cox contributed to this story.