Cook on Thursday also asked for a temporary restraining order declaring that Trump’s attempt to fire her is unlawful and preventing the Fed from removing her for now.
A hearing on that motion has been set for Friday morning.
White House spokesman Kush Desai maintained in a statement on Thursday that Trump had “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”.
Mortgage receipts were “very clearly shown to the President”, added White House Press Secretary Karoline Leavitt.
Among the alleged false statements was that Cook had claimed two primary residences, one in Michigan and another in Georgia.
Cook has not been charged with a crime and the alleged incidents occurred before she was in her current position.
Trump’s move marked a dramatic escalation in his effort to exert control over the Fed, in a step that could put the institution’s independence at risk, according to analysts.
Cook’s lawsuit stressed that Fed independence “is vital to its ability to make sound economic decisions, free from the political pressures of an election cycle”.
For months, the US leader has been calling for the bank to slash interest rates, lashing out repeatedly at Fed Chairman Jerome Powell for being “too late” and calling him a “moron”.
But policymakers had been holding rates steady as they monitored the effects of Trump’s fresh – and sweeping – tariffs on consumer inflation.
By removing Cook, Trump could add another voice to the Fed’s board to try and shift interest rates in his favoured direction.
A Fed spokesperson has earlier said that the central bank “will abide by any court decision”.
The legal dispute marks the latest test of presidential powers under Trump’s new White House term, with the 79-year-old Republican – backed by loyalists throughout the Government – forcefully moving to exert executive authority.
But even as the Supreme Court’s conservative majority recently allowed Trump to fire members of other independent government boards, it created a carveout for the Fed in its ruling.
Federal law says Fed officials can only be removed for “cause”, which could be interpreted to mean malfeasance or dereliction of duty.
– Agence France-Presse