(Reuters) -The U.S. Justice Department has launched a criminal mortgage fraud probe into Federal Reserve Governor Lisa Cook and has issued grand jury subpoenas out of both Georgia and Michigan, according to documents seen by Reuters and a source familiar with the matter.

The investigation, which followed a criminal referral from Federal Housing Finance Agency Director Bill Pulte, is being conducted by Ed Martin, who was tapped by Attorney General Pam Bondi as a special assistant U.S. attorney to assist with mortgage fraud investigations involving public officials, along with the U.S. Attorneys' offices in the Northern District of Georgia and the Eastern District of Michigan, according to the person, who spoke anonymously since the matter is not public.

Pulte, who was appointed by Trump, has accused Cook of committing fraud by listing more than one property as a primary residence when she applied for mortgages, potentially to secure lower interest rates. Cook owns properties in Michigan, Georgia and Massachusetts.

Trump terminated Cook over Pulte's mortgage fraud allegations against her, prompting her to file a lawsuit challenging his effort to oust her.

Cook's lawyer, prominent Washington attorney Abbe Lowell, said the Justice Department was scrambling to invent new justifications for Trump's overreach in firing the Fed governor.

"He wants cover, and they are providing it. The questions over how Governor Cook described her properties from time to time, which we have started to address in the pending case and will continue to do so, are not fraud, but it takes nothing for this DOJ to undertake a new politicized investigation, and they appear to have just done it again," Lowell said.

The case, which will likely end up before the U.S. Supreme Court, has ramifications for the Fed's ability to set interest rate policy without regard to politicians' wishes, widely seen as critical to any central bank's ability to keep inflation under control.

Trump has demanded that the U.S. central bank cut rates immediately and aggressively, berating Fed Chair Jerome Powell for his stewardship of monetary policy.

In one of her recent legal filings challenging Trump's actions, Cook said she listed mortgages on three properties on forms submitted to the White House and U.S. Senate in the vetting process for her appointment to the Fed in 2022. Any inconsistencies were known when she was confirmed and cannot give Trump grounds to fire her now.

Cook is the third public official to be targeted in a criminal investigation over mortgage fraud allegations.

Martin, who also presides over the "Weaponization Working Group" and serves as pardon attorney, is also pursuing criminal probes into Democratic U.S. Senator Adam Schiff as well as New York Attorney General Letitia "Tish" James. There are also grand juries convened in those two cases, which started prior to Martin's new appointment as a special assistant U.S. attorney, according to the source and documents seen by Reuters.