Federal Reserve governor Lisa Cook has sued President Donald Trump over his attempt to fire her, setting up a potential legal battle with implications for 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 as defendant.

Trump has said there was 'sufficient reason' to believe Cook had made false statements on her mortgage, citing constitutional powers that allow him to remove her. Cook previously stated that 'no cause exists under the law' to sack 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 several legal challenges that could reach 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 be the first of its kind in the Board's history, Abbe Lowell, Cook's attorney, wrote in the lawsuit.

He further argued, It would subvert the Federal Reserve Act ... which explicitly requires a showing of 'cause' for a Governor's removal, which an unsubstantiated allegation regarding private mortgage applications submitted by Governor Cook prior to her Senate confirmation is not.

White House spokesperson Kush Desai stated the president 'exercised his lawful authority to remove' Cook, explaining that there was cause to dismiss an official 'credibly accused of lying in financial documents' related to her role overseeing financial institutions.

The Federal Reserve Act stipulates that the president does not have the authority to remove a Fed official at will, yet it does permit dismissal 'for cause'.

The allegations against Cook were initially made in a public letter from Bill Pulte, a housing finance regulator and Trump ally, accusing Cook of falsifying records to secure a mortgage. Cook denies any wrongdoing, and no charges have been brought against her.

Trump's attempt to remove Cook comes as he expresses frustration with the Fed over interest rates, indicating a desire for more favorable policies aligned with his economic agenda.

This situation has broader implications considering the Fed's significant role in determining interest rates, which affects consumer borrowing and saving, as well as influencing monetary policies in other countries.