By Bryan Mena, CNN

Washington (CNN) — President Donald Trump on Wednesday called on a top policymaker at the Federal Reserve to resign, after one of his allies alleged that she committed mortgage fraud.

In a letter dated August 15, Federal Housing Finance Agency director Bill Pulte urged the Justice Department to investigate a pair of mortgages taken out in recent years by Fed Governor Lisa Cook.

On Wednesday, Trump referenced those allegations on his social media platform, writing that “Cook must resign, now!!!”

But Cook pushed back on calls to resign, saying she would not be pushed out of the Fed.

“I learned from the media that FHFA Director William Pulte posted on social media that he was making a criminal referral based on a mortgage application from four years ago, before I joined the Federal Reserve,” Cook wrote in a statement.

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

Pulte, a vocal Trump ally, has frequently criticized the Fed and its leader, Chair Jerome Powell, for not lowering rates. He also called for closer scrutiny of the central bank’s costly refurbishment of its Washington, DC, headquarters.

“She needs to explain herself, but it’s all there in black and white,” Pulte said in a phone interview with CNBC on Wednesday. “I think she needs to resign quickly.”

The new focus on Cook is an expansion of the Trump administration’s intense pressure campaign against the Fed, specifically central bankers who aren’t perceived as allies of the president.

Trump is still loudly demanding the Fed lower interest rates, continuing to bash Powell with the moniker “Too Late.” After raising rates in recent years to fight pandemic inflation that reached 40-year highs in 2022, the central bank started to cut its benchmark lending rate last fall. While inflation earlier this year hovered close to the bank’s target rate of 2%, central bankers have paused further rate cuts while they ascertain the economic impact of Trump’s tariffs.

In the letter, which Pulte posted on social media, he alleged that Cook, a Biden appointee, “falsified bank documents and property records to acquire more favorable loan terms, potentially committing mortgage fraud under the criminal statute.”

Pulte refers to a mortgage Cook took out in June 2021 to purchase a property in Ann Arbor, Michigan, which stipulated it would be her primary home address for at least a year, according to the letter. Cook then took out another mortgage in Georgia two weeks later, Pulte said, also declaring that property as her primary home address. Cook’s Georgia home was later listed as a rental, according to Pulte.

The housing official has functioned as a reliable attack dog for the Trump administration, routinely taking to social media to berate Powell, essentially around the clock. Sen. Elizabeth Warren of Massachusetts has criticized Pulte’s incessant use of social media for political attacks.

But Pulte told CNBC that his call for Cook to resign was apolitical.

“There can be no mortgage fraud. This came across our desk, and it’s my duty to report it,” Pulte said. “It wouldn’t matter if she were a Republican or a Democrat. It is what it is.”

The Fed declined CNN’s request for comment.

As Cook faces pressure, the Senate Banking Committee is expected to soon consider Trump’s nomination of Stephen Miran, head of the Council of Economic Advisers, to fill the vacancy on the central bank’s board left by Fed Governor Adriana Kugler, a Biden appointee.

“We see a window for the Senate to confirm Stephen Miran as a Fed governor, but question if Lisa Cook has an incentive to resign before the meeting. Either way, we see limited impact as the (Fed’s rate-setting committee’s) membership is broader than just Federal Reserve Board members,” Jaret Seiberg, an analyst at TD Cowen Washington Research Group, wrote in commentary issued Wednesday.

“For Cook, resigning will not end the legal probe. It is why we see no incentive for her to react to Pulte by departing before the next (Fed) meeting,” he said.

If Cook were to resign from the Fed’s board, that would leave only two governors appointed solely by a Democratic president out of a total of seven seats: Fed Governor Michael Barr and Fed Vice Chair Philip Jefferson. Kugler stepped down from her governor position earlier this month. Powell has been appointed to Fed roles by Democratic and Republican presidents, and his term as chair ends in May 2026, though his position as a governor stretches to 2028.

Cook is the first Black woman appointed to the Fed’s Board of Governors.

The Trump administration’s latest attacks come as Fed policymakers convene in Jackson Hole, Wyoming, for an annual economics symposium hosted by the Federal Reserve Bank of Kansas City, seen as a major event for the world’s central bankers and US monetary policy.

During his keynote speech at the conference, Powell is widely expected to signal long-awaited rate cuts in the second half of the year, citing fragility in the labor market, which is the theme of the symposium. Financial markets are pricing in a roughly 83% chance of a rate cut at the Fed’s September meeting, according to futures.

Since Trump began his second term, Powell has resisted the president’s demands to lower rates and has mostly refrained from responding to his personal attacks. Trump recently backed off from his threats to fire Powell, though it would have led to an uphill battle in the courts if he were to try.

“It looks to me like the administration is admitting they can’t push Powell out or push him around,” said Joe Brusuelas, chief economist at RSM US. “Moreover, they realize that even when they appoint his successor, there is no guarantee they achieve their preferred policy outcome.”

“They are going to need to create the conditions where they can replace enough members to get the votes they want,” he added.

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CNN’s David Goldman and Matt Egan contributed to this report.