On Wednesday, Mr. Pulte said on social media that his agency had made a criminal referral to the Justice Department alleging that Ms. Cook committed mortgage fraud.

U.S. President Donald Trump on Friday said he would fire Federal Reserve Governor Lisa Cook if she doesn't resign.

In a statement released by the Fed on Wednesday, she said she had “no intention of being bullied” and pledged to gather “accurate information to answer any legitimate questions and provide the facts....