An emergency court hearing over President Donald Trump's attempt to fire Federal Reserve governor Lisa Cook ended without a ruling on Friday.

Cook's lawyers requested a temporary restraining order to block Trump from removing her from role, calling the president's firing "unlawful and void".

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 case sets off a potential legal battle, which could reach the Supreme Court, with implications for the US central bank's independence.

Cook's lawyer, Abbe Lowell, spent a portion of his remarks arguing Cook should stay in her job as the lawsuit plays out.