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.

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.

Ms. Cook said that she would not resign from the board of governors, hours after President Trump announced he was firing her.