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, and cited constitutional powers which he said allowed him to remove her. Cook previously stated that no cause exists under the law to sack her.

The president's frustration with the Fed's interest rate policies has been evident, as he has been increasingly vocal about what he perceives as a reluctance to lower rates.

Cook is part of the board responsible for setting interest rates in the US. The lawsuit is anticipated to raise significant legal questions that may ascend to 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, said Abbe Lowell, Cook's attorney, in the lawsuit.

The lawsuit emphasizes that the Federal Reserve Act mandates that a valid cause must be shown for the removal of a Governor, which an unverified claim regarding private mortgage documents cannot fulfill.

White House spokesperson Kush Desai remarked that the president exercised his lawful authority to remove Cook, citing allegations of falsehoods in financial documents.

Cook has denied any wrongdoing related to allegations made in a public letter by housing finance regulator Bill Pulte, who is associated with Trump. Pulte's claims suggested that Cook signed contradictory documents regarding the primary residence status of two homes.

The outcome of this lawsuit could significantly impact the political landscape, especially considering that Trump has the power to nominate Cook's successor, who would likely align more closely with his economic policies.

The Federal Reserve's decisions regarding interest rates carry considerable weight, influencing borrowing costs and savings rates across the nation.