By Bryan Mena, Phil Mattingly, CNN

Washington (CNN) — A Justice Department official is set to probe Federal Reserve Governor Lisa Cook after she was accused by a member of President Donald Trump’s administration of committing mortgage fraud, according to a letter sent Thursday to Fed Chair Jerome Powell.

The letter, seen by CNN, was written by Ed Martin, a lawyer at the department who’s tasked with investigating mortgage fraud. Martin said the situation “requires further examination.”

In a letter dated August 15, Federal Housing Finance Agency Director Bill Pulte said that Cook claimed two properties — a home in Michigan and a condo in Atlanta — as her primary home addresses. On Thursday, he said on social media the administration is “probing a 3rd property owned by Cook.”

Pulte, a vocal Trump ally, said in an interview with Bloomberg earlier on Thursday that he looked into Cook, a then-President Joe Biden appointee, based off a tip. He added that his agency has used artificial intelligence software from Palantir to track potential mortgage fraud.

In his letter, Martin also said: “I encourage you to remove Ms. Cook from your Board. Do it today before it is too late!”

“After all, no American thinks it is appropriate that she serve during this time with a cloud hanging over her,” he said.

However, only the president has the power to remove a Fed official — and only for cause. In a response to Pulte’s accusations, Cook was defiant, saying in a statement that she has “no intention of being bullied to step down from my position because of some questions raised in a tweet.”

She added that she is “gathering the accurate information to answer any legitimate questions and provide the facts.” According to documents reviewed by CNN, the 2021 mortgage Cook took out to purchase a home in Ann Arbor, Michigan was for $203,000 plus interest, and it stipulated that she had to occupy it as her “principal residence” within 60 days of the loan being executed.

The Fed declined CNN’s request for comment.

“I believe she did sign these documents. Is it mortgage fraud to say that you live in one area and not another area? Yes, it is mortgage fraud,” Pulte told Bloomberg. “People in power especially have a responsibility to read legal documents before they sign them.”

Pulte said his accusations aren’t political and that he would go after anyone suspected of committing mortgage fraud, whether they are Republican or Democrat. However, the Trump administration has focused on investigating public figures seen as adversaries of the president, such as New York Attorney General Letitia James and Sen. Adam Schiff of California.

And those investigations, led by Martin, have been carried out in an unusual way. In video previously reported by CNN, Martin was seen posing for photos outside of James’ home after he sent a letter to her attorney, Abbe Lowell, urging James to resign.

Like Pulte, Martin is also seen as a reliable attack dog for the Trump administration. In media interviews he’s talked about investigating Trump’s enemies, even though Justice Department policy generally prohibits discussing criminal probes publicly.

Since the beginning of his second term, Trump has waged an intense pressure campaign against the Fed because central bankers haven’t lowered borrowing costs this year. Trump’s attacks have mostly been focused on Powell, but now the president is blasting Cook, a Biden appointee.

It’s unclear whether Trump and his allies will ultimately move forward with building a case to sack Cook for cause, which would tilt the make-up of the Fed in Trump’s favor.

If Cook were to be removed 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. Stephen Miran, chair of the Council of Economic Advisers, has been nominated to fill a vacant seat left by former Fed Governor Adriana Kugler after she resigned earlier this month.

“The Fed board is comprised of seven governors, one of them the chairman. With a four-person majority, the Board can fire regional Fed bank presidents who play a key role in interest rate decisions,” Jon Hilsenrath, senior adviser at brokerage firm StoneX, wrote in a statement on LinkedIn Thursday.

“Each one of these board seats matters a great deal to a president who wants to reshape how the central bank works and what it decides. Getting rid of Cook would be a way for the President to build that four-person majority,” he added.

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CNN’s Samantha Delouya contributed reporting.