(Reuters) -The U.S. Supreme Court announced on Wednesday that it will hear arguments on January 21 in President Donald Trump's attempt to remove Federal Reserve Governor Lisa Cook, a move without precedent that challenges the central bank's independence.

The justices said in October that they would hear arguments in the case before deciding a Justice Department request to lift a judge's order that temporarily blocked the Republican president from removing Cook, an appointee of Democratic former President Joe Biden. That action effectively left Cook in place for the time being. 

In creating the Fed in 1913, Congress passed a law called the Federal Reserve Act that included provisions to shield the central bank from political interference, requiring governors to be removed by a president only "for cause," though the law does not define the term nor establish procedures for removal. The law has never been tested in court.

Washington-based U.S. District Judge Jia Cobb on September 9 ruled that Trump's claims that Cook committed mortgage fraud before taking office, which Cook denies, likely were not sufficient grounds for removal under the Federal Reserve Act.

Cook, the first Black woman to serve as a Fed governor, sued Trump in August after the president announced he would remove her - the first time a president has sought to oust a Fed official. Cook has said the claims made by Trump against her did not give the president the legal authority to remove her and were a pretext to fire her for her monetary policy stance.

In her first public appearance since Trump moved to fire her, Cook said on November 3 it takes "thick skin" to pursue public service in the United States.

Fed independence "is something worth pursuing," Cook said at a Washington-based think tank. "This too shall pass. I will continue doing this work on behalf of the American people."

The U.S. Court of Appeals for the District of Columbia Circuit in a 2-1 ruling on September 15 denied the administration's request to put Cobb's order on hold.

The Supreme Court has in a series of decisions in recent months allowed Trump to remove members of various federal agencies that Congress had established as independent from direct presidential control despite similar job protections for those posts.

Those decisions suggest that the court, which has a 6-3 conservative majority, may be ready to jettison a key 1935 precedent that preserved these protections in a case that involved the U.S. Federal Trade Commission.

But in Cook's case, the court opted to hear arguments first before deciding the Justice Department's request to similarly remove Cook on a preliminary basis.

The court already signaled that it could treat the Fed as distinct from other executive branch agencies, noting in May in a case involving Trump's dismissal of two Democratic members of federal labor boards that the Fed "is a uniquely structured, quasi-private entity" with a singular historical tradition.

Based on the arguments in January, the court will decide whether Cook can stay in her post or must go while her legal challenge to her firing proceeds in lower courts. 

Also on Wednesday, the court set January 13 for oral arguments in appeals by Idaho and West Virginia seeking to enforce state bans on transgender athletes participating on female sports teams at public schools.