President Donald Trump demanded on Wednesday that Federal Reserve Governor Lisa D. Cook resign, citing a referral from Federal Housing Finance Agency Director Bill Pulte that urges the Justice Department to investigate the governor for possible mortgage fraud. In a social-media post, Trump wrote, “Cook must resign, now,” escalating his long-running efforts to remake the leadership of the U.S. central bank. Pulte’s 15-August letter to Attorney General Pam Bondi alleges Cook declared both her Ann Arbor, Michigan, home and an Atlanta condominium as primary residences in mid-2021, a move that could have secured more favorable loan terms and violated federal fraud statutes. A Justice Department official confirmed the referral has been received and is being taken “very seriously.” Cook and the Federal Reserve declined to comment. Cook, the first Black woman on the Fed board and a 2022 appointee of President Joe Biden, is serving a term that runs to 2038. Her departure would give Trump a fifth pick on the seven-member board, tilting the balance toward his nominees as he presses the Fed to lower interest rates. The Wall Street Journal reported Trump has told aides he may attempt to fire Cook for cause if she refuses to step down. The dollar weakened modestly after Trump’s remarks, reflecting investor concern over heightened political pressure on the independent central bank. No charges have been filed, and the Justice Department has not said whether it will open a formal investigation.