President Donald Trump has fired Federal Reserve Governor Lisa Cook, a sharp escalation in his battle to exert greater control over what has long been considered an institution independent from day-to-day politics.

I have determined that there is sufficient cause to remove you from your position,” Mr. Trump said in a letter. Her dismissal threatened to touch off a landmark legal battle over the Fed’s independence.

President Donald Trump on Monday said he has fired Federal Reserve Governor Lisa Cook, according to a letter addressed to her posted on his social media — the first instance of a president firing a central bank governor in the central bank’s 111-year history.