A Federal Reserve governor, Lisa Cook, says in a new Supreme Court filing that President Trump is trying to “eviscerate the independence” of the Federal Reserve Board.

Lawyers for Ms. Cook tell the high court that her firing was based on “flimsy, unproven allegations of pre-office wrongdoing—allegations conveniently timed following the President’s criticism of the Board’s policy decisions.”

“And as the Court recognized earlier this year, the Board’s independence is uniquely entrenched in the Nation’s history and tradition,” the filing goes on to say. “Yet the President now requests that the Court precipitously depart from that view and allow him to remove Governor Lisa D. Cook from the Federal Reserve Board.”

Ms. Cook is responding to an emergency application by the president for her removal from the Fed as she continues her legal fight to keep her job.

Mr. Trump and his administration have accused Ms. Cook of committing mortgage fraud, citing documents related to two properties Ms. Cook allegedly claimed as primary residences. Some documents show that she claimed one residence as a vacation home and the other as her primary residence, Reuters reported.

Mr. Trump attempted to fire Ms. Cook on August 25. A district court judge blocked Ms. Cook’s immediate firing.

The U.S. Court of Appeals for the District of Columbia Circuit ruled that it would not remove Ms. Cook because the court believes that she has not been given the proper amount of time to respond to the presidency’s accusations.

“The district court thus preliminarily enjoined Cook’s removal based, in part, on its conclusion that her removal likely violated the Fifth Amendment’s Due Process Clause. That conclusion is correct,” the appeals court found.

President Trump then appealed to the Supreme Court. The Department of Justice, in its appeal, accuses the lower court jurists of committing “improper judicial interference with the President’s removal authority.”

Citing Mr. Trump’s vast powers as president, justice department lawyers argue that judges had no right to review his firing of Ms. Cook at all. Government lawyers argue that federal statutes are vague enough to allow Mr. Trump to remove Ms. Cook, so long as he identifies some reason other than a policy disagreement.

Ms. Cook is getting a lot of support in friend of the court filings in the case. Every living former head of the Federal Reserve and other former leading policymakers are asking the Supreme Court to preserve the independence of the central bank and allow Ms. Cook to stay in her role as she fights her firing by Mr. Trump.

A friend-of-the-court brief filed on Thursday supporting Ms. Cook also has the support of a group of former Treasury secretaries, Federal Reserve governors, Council of Economic Advisers chairmen, and economists.

The brief in support of Ms. Cook says granting the government’s request to remove her immediately would upset longstanding protections of the Federal Reserve. “Doing so would expose the Federal Reserve to political influences, thereby eroding public confidence in the Fed’s independence and jeopardizing the credibility and efficacy of U.S. monetary policy,” the brief — signed by three former Fed leaders, Janet Yellen, Ben Bernanke, Alan Greenspan, and others — states.

“Maintaining the status quo while the lawfulness of the termination is adjudicated, in contrast, would serve the public’s interest by safeguarding the independence and stability of the system that governs monetary policy in this country.”

The attorney general of Florida and his colleagues in 21 other Republican-controlled states submitted their own brief supporting Mr. Trump’s removal. They claim that temporarily reinstating Ms. Cook “will cause the government “irreparable harm” that outweighs any harm due to her absence.

Ms. Cook has not been charged or convicted in connection with the mortgages. Her own response to the Supreme Court was due on Thursday afternoon.