WASHINGTON, United States (AFP) — A  United States (US) court on Friday began hearing Federal Reserve Governor Lisa Cook’s challenge of President Donald Trump’s attempt to fire her, in a legal battle set to have major implications for the US central bank and its independence.

In the first hearing in the case, a judge in Washington considered Cook’s request for a temporary order declaring Trump’s attempt to oust her unlawful.

This would allow Cook — the first Black woman to serve on the Fed’s board — to continue in her role while she challenges her ouster.

The session closed without a ruling Friday, with more arguments to be submitted Tuesday.

Judge Jia Cobb heard arguments from lawyers representing Cook and Trump respectively, with discussions surrounding whether it mattered that the alleged transgressions had taken place before she became a Fed governor.

Critics accuse Trump of seeking to fire Cook in order to tip the Fed’s board in favour of his stated goal of lowering interest rates.

The hearing also touched on whether Cook was given sufficient notice before Trump took action to remove her and whether the president’s motivation in firing her was relevant to the case.

In a recent ruling, the Supreme Court suggested that Fed officials can only be removed for “cause,” which could be interpreted to mean malfeasance or dereliction of duty.

On Monday evening, Trump published a letter on his Truth Social platform saying that he was immediately removing Cook over claims of mortgage fraud.

Among the allegations were that Cook had claimed two primary residences, one in Michigan and another in Georgia.

Trump pointed to a criminal referral dated August 15 from Federal Housing Finance Agency (FHFA) director Bill Pulte in announcing Cook’s removal.

Cook has not been charged with a crime, and the alleged incidents occurred before she was in her current position.

The president’s lawyers argued in a filing Friday that he had also given Cook ample notice, saying that he publicised the FHFA referral on August 20.

But Cook’s lawyer countered that allegations of fraud have become a “weapon of choice” to remove officials.

He noted that Trump had been calling Fed Chair Jerome Powell “too late” in lowering interest rates before directing his ire at Cook.

Late Thursday, Pulte wrote on social media that the FHFA had sent a second criminal referral to US authorities, claiming further misrepresentations about Cook’s properties.

Cook’s attorney Abbe Lowell pushed back in a separate statement that this was “an obvious smear campaign” by a “political operative” aimed at discrediting Cook.

“Nothing in these vague, unsubstantiated allegations has any relevance to Gov Cook’s role at the Federal Reserve, and they in no way justify her removal from the Board,” Lowell said.

Should Cook win the case, the president’s ability to force Fed officials out of the central bank will be limited, in a boost to the institution’s independence.

But her loss could allow the opposite to occur, in a blow to the organisation and with major implications for the world’s biggest economy.