Federal Reserve governor Lisa Cook has sued President Donald Trump over attempt to fire her, setting up a potential legal battle over the US central bank’s autonomy.

Cook has asked the court to declare Trump’s firing order “unlawful and void”, and also named Fed Chairman Jerome Powell and the Board of Governors as defendants.

Trump has said there was “sufficient reason” to believe Cook had made false statements on her mortgage, and cited constitutional powers which he said allowed him to remove her.

The president has put increasing pressure on the Fed over what he sees as an unwillingness to lower interest rates. Cook is part of the board responsible for setting interest rates in the US.

Thursday’s lawsuit is likely to bring up a number of legal challenges that could end up at the US Supreme Court.

“This case challenges President Trump’s unprecedented and illegal attempt to remove Governor Cook from her position which, if allowed to occur, would the first of its kind in the Board’s history,” Abbe Lowell, Cook’s attorney, wrote in the lawsuit.

“It would subvert the Federal Reserve Act … which explicitly requires a showing of ’cause’ for a Governor’s removal, which an unsubstantiated allegation about private mortgage applications submitted by Governor Cook prior to her Senate confirmation is not,” Lowell wrote.

White House spokesperson Kush Desai told the BBC the president “exercised his lawful authority to remove” Cook.

“The President determined there was cause to remove a governor who was credibly accused of lying in financial documents from a highly sensitive position overseeing financial institutions,” he said. “The removal of a governor for cause improves the Federal Reserve Board’s accountability and credibility for both the markets and American people.”

The allegations against Cook were first made in a public letter from housing finance regulator, Bill Pulte, a Trump ally. In the letter he accused Cook of falsifying records to obtain a mortgage.

The letter alleges that she signed two documents, two weeks apart, attesting that two homes in different states were both her primary residence. No charges have been brought against Cook and it is unclear if she is under investigation for these allegations.

Cook’s lawsuit does not address those allegations.

She is one of seven members of the Fed’s board of governors, and in this position sits on the 12-member committee which is responsible for setting interest rates in the US.

Since returning to Washington, Trump has put increasing pressure on the Fed – especially Powell – over interest rates.