President Donald Trump has said he will immediately remove Federal Reserve official Lisa Cook from her position, a major escalation in his battle against the US central bank.

In an announcement made on his social media platform Truth Social, Trump posted a letter addressed to Cook in which he informed her of his decision to remove her from the bank's board of governors with immediate effect.

He said there was "sufficient reason" to believe she had made false statements on mortgage agreements, and cited constitutional powers which he said allowed him to remove her.

Neither Cook or the Federal Reserve has commented on the sacking, which the president announced late on Monday.

Trump has put increasing pressure on the Fed - especially its chair Jerome Powell - in recent weeks over what he sees as the central bank's unwillingness to lower interest rates. He has repeatedly floated the possibility of firing Powell.

His decision to fire Cook, who is one of seven members of the Fed's board of governors and the first African American woman to serve in the role, is believed to be unprecedented in the central bank's 111-year history.

It is also likely to raise legal questions, with experts suggesting the White House will need to demonstrate - potentially in court - that it had sufficient reason to fire her.

According to Trump's letter, Cook signed one document attesting that a property in Michigan would be her primary residence for the next year.

"Two weeks later, you signed another document for a property in Georgia stating that it would be your primary residence for the next year," the president said.

"It is inconceivable that you were not aware of your first commitment when making the second," he wrote.

The president had called for her resignation last week over the allegation of mortgage fraud, which was first made in a public letter from housing finance regulator, Bill Pulte, a Trump ally, to Attorney General Pam Bondi.

The housing finance regulator called the letter a "criminal referral" and urged the justice department to investigate. It is not clear whether an investigation has been opened.

Cook told the BBC in a statement last week that she learned of the allegations from the media, and the matter stemmed from a mortgage loan application she made four years ago before she joined the central bank.

"I have no intention of being bullied to step down from my position because of some questions raised in a tweet," she said.

"I do intend to take any questions about my financial history seriously as a member of the Federal Reserve and so I am gathering the accurate information to answer any legitimate questions and provide the facts."

If Cook or the Fed resist Trump's decision to oust her, experts suggest it could trigger a standoff between the central bank and the White House. The Fed gained independence from the US government in 1951.

Trump has expressed increasing animosity at Powell, calling him a "numbskull" and a "stubborn moron" because he did not support the president's calls for rapid, large cuts to borrowing rates.

But last week, Powell boosted expectations that there will be an interest rate cut in September. Speaking to central bankers gathered in Jackson Hole, Wyoming, he also argued that the inflationary impact of Trump's tariffs could prove temporary.