(Reuters) -A federal judge on Friday said she would set an expedited briefing schedule in Federal Reserve Governor Lisa Cook's bid to temporarily block President Donald Trump from firing her while she pursues a lawsuit that says he has no valid reason to remove her from the U.S. central bank.

The hearing before U.S. District Judge Jia Cobb in Washington, D.C., is the first step in what will likely be a protracted legal battle that could upend the Fed's historical independence and is likely to be resolved by the U.S. Supreme Court.

Cook sued Trump and the Fed on Thursday, saying the Republican president's unsubstantiated claim she engaged in mortgage fraud before taking office did not give him legal authority to remove her, and was a pretext to fire her for refusing to lower interest rates.

The Fed governor has called the allegations "unsubstantiated and unproven" but has not explained the basis for that position.

Concerns about the Fed's independence from the White House in setting monetary policy could have a ripple effect throughout the global economy. The U.S. dollar stumbled against other major currencies after Trump said he would remove Cook.

The law that created the Fed says governors may be removed only "for cause," but does not define the term nor establish procedures for removal. No president has ever removed a Fed governor, and the law has never been tested in court.

Cook's emergency motion to block her removal pending further litigation is being taken up by Cobb, an appointee of Democratic former President Joe Biden.

To rule in favor of Cook, Cobb would have to find that her lawsuit is likely to succeed, that Cook faces irreparable harm if she is removed and that such a ruling is in the public interest.

Cook, in court filings, denied committing mortgage fraud but said that even if she had, it would not be grounds for removal because the alleged conduct occurred before she was confirmed by the U.S. Senate and took office in 2022.

Trump claims that Cook described separate properties in Michigan and Georgia as primary residences on mortgage applications in 2021, which could have allowed her to obtain lower interest rates.

SUFFICIENT CAUSE

Trump administration lawyers argued in a Friday court filing that alleged mortgage fraud is sufficient cause to remove a Fed governor, regardless of when it happened.

The president and William Pulte, the Trump-appointed director of the Federal Housing Finance Agency who first raised questions about Cook's mortgages earlier in August, have said the alleged conduct calls her integrity into question.

The administration also argued that giving Fed governors protections from removal violates the president's broad constitutional powers to control the executive branch, as it has in lawsuits filed by other ex-officials that Trump has fired.

Cook counters that federal laws limiting the president's ability to remove officials from other agencies define cause as negligence, malfeasance or inefficiency that occurs when an official is in office, and the same standard should apply to the Fed.

"There is no conceivable interpretation of 'for cause' removal protection that would allow the President to fire Governor Cook, either for his true motive or the pretextual one he has invented," she said in the motion seeking a temporary restraining order.

Such orders cannot generally be appealed, but if Cobb sides with Cook, she would likely issue a longer-term preliminary injunction that could be reviewed by an appeals court.

The Fed said on Friday in a court filing that it takes no position on the lawsuit but that it wants a "prompt ruling" in order to remove "the existing cloud of uncertainty."

The case will likely reach the U.S. Supreme Court, where a conservative majority has tentatively allowed Trump to fire officials from other agencies despite laws shielding them from removal.

But the court in a May order distinguished the Fed from those agencies, citing its unique structure and "distinct historical tradition."

Cook's departure would allow Trump to name his fourth pick to the Fed's seven-member board.

The president has repeatedly berated Fed Chair Jerome Powell for not lowering rates and allegedly mishandling a multibillion-dollar renovation project, though he has stopped threatening to remove Powell before his term as central bank chief ends in May.

The Fed is widely expected to cut interest rates at its September 16-17 policy meeting.