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.

"She should not be taken out of her office, she shouldn't be disconnected from her electronics," he said. "She should do all the things that she did a week ago before all this started, because that is the status quo."

Yaakov Roth, a top Justice Department attorney, argued that there were grounds to dismiss Cook and said that the president's desire to remove her from her job were not tied to having more sway over the Federal Reserve.

Since returning to the White House, Trump has put increasing pressure on the Fed - especially its chair Jerome Powell - over what he sees as an unwillingness to lower interest rates.

Cook voted alongside Powell and most other members of the committee to maintain US interest rates at the Fed's last rate-setting meeting at the end of July.

Trump's attempt to remove Cook has prompted concern that investors could begin to doubt the credibility of the Fed. If that happens, borrowing costs for the US government could rise - and that would have knock-on effects around the world since they are used to set the price of assets.

Much of Friday's arguments focused on whether or not Trump had "cause" to remove Cook from her job.

The Federal Reserve Act does not give the president authority to remove a Fed official at will, but as Trump has said, it does allow him to do so "for cause".

Mr. Roth said that "cause" is "more than a mere policy disagreement" and is dependent on a person's ability to the do a job.

He argued that a "very senior financial regulatory official" who makes "contradictory" statements on financial documents could constitute reasonable cause for removal.

Cook was accused of falsifying records to obtain a mortgage, in a public letter from housing finance regulator, Bill Pulte, a Trump ally.

The letter alleges that she signed two documents, two weeks apart, attesting that two homes in different states were both her primary residence. No charges have been brought against Cook.

Cook's lawsuit does not address the mortgage allegations. (BBC)