Lisa Cook, a governor on the Federal Reserve Board, sued President Trump on Thursday over his decision to fire her from the nation’s central bank, arguing that she should be able to retain her position because the White House had no authority to order the dismissal.

Ms. Cook’s lawsuit, which was filed in the U.S. District Court for the District of Columbia, described her ouster as “unprecedented and illegal,” as she framed Mr. Trump’s actions as part of an overtly political campaign to pressure the independent Fed into lowering interest rates.

The lawsuit sets the stage for a landmark legal battle over the future of the Fed, an independent institution that Mr. Trump has savaged for months in a bid to install new political loyalists who share his views on monetary policy.

Ms. Cook also listed the Fed’s Board of Governors and Jerome H. Powell, its chair, as defendants alongside Mr. Trump. That reflected their ability to take actions that carried out the president’s orders, the lawsuit said. In a statement earlier this week, the Fed said that it would “abide by any court decision.” Until the court rules, Ms. Cook is still considered an active governor.

Ms. Cook officially embarked on her legal campaign three days after Mr. Trump announced that he would fire her in a letter posted to social media. The president claimed that Ms. Cook, who was confirmed by the Senate in 2022, had engaged in mortgage fraud, as he invoked a power in the Fed’s founding statute that allowed him to dismiss governors for cause.

But Ms. Cook, the first Black woman to serve as a Fed governor, has not been charged or convicted of any crime. Many experts questioned the legality of Mr. Trump’s actions, pointing out that the allegations against Ms. Cook were unproven and involved conduct that predated her time at the Fed. Nor was Ms. Cook afforded an opportunity to review the evidence and respond to the claims formally, which struck many observers as legally problematic.