Washington DC - Federal Reserve Governor Lisa Cook rejected President Donald Trump's unprecedented bid to oust her on Tuesday, saying he had no legal authority for such an intervention against a member of the independent central bank.

After calling for her resignation last week, Trump posted a letter on Monday evening to his Truth Social platform purporting to have fired Cook "effective immediately."

The decision cited allegations of false statements on her mortgage agreements, claiming "there is sufficient cause to remove you from your position."

"I will not resign," said Cook, the first Black woman to serve on the central bank's board, in a statement shared with AFP by her attorney Abbe Lowell.

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"President Trump purported to fire me 'for cause' when no cause exists under the law, and he has no authority to do so," she added.

Lowell pledged to "take whatever actions are needed to prevent his (Trump's) attempted illegal action."

The potential legal dispute would be the latest test of presidential powers under Trump's new term, with the 79-year-old Republican – backed by loyalists throughout the government – forcefully moving to exert executive authority.

The Supreme Court's conservative majority recently allowed Trump to fire members of other independent government boards, but notably created a carveout for the Federal Reserve in its ruling.

Federal law says that Fed officials can only be removed for "cause," which could be interpreted to mean malfeasance or dereliction of duty.

In his announcement that Cook would be removed, Trump pointed to a criminal referral dated August 15 from the Federal Housing Finance Agency's director – a staunch ally of Trump – to the US attorney general.

The referral, Trump said, provided "sufficient reason" to believe that Cook might have made "false statements" on one or more mortgage agreements.

One of 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 false statements occurred before she was in her current position.

Earlier this month, Cook said in a statement that she had "no intention of being bullied to step down," but would take questions about her financial history seriously.