US President Donald Trump on Wednesday called on Federal Reserve Governor Lisa Cook to resign on the basis of allegations made by one of his political allies about mortgages she holds in Michigan and Georgia, intensifying his effort to gain influence over the US central bank.

"Cook must resign, now!!!" Trump wrote on his Truth Social platform, sharing a Bloomberg news report on how the Federal Housing Finance Agency's director has called for greater scrutiny of Cook over a pair of mortgages.

Cook said she had "no intention of being bullied to step down" from her position at the central bank after US Federal Housing Finance Agency Director William Pulte raised the allegations 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 said in a statement.

Trump has also told aides he is considering trying to fire Cook, the first Black woman to serve on the Fed board, the Wall Street Journal reported on Wednesday, citing a senior White House official and another person familiar with the matter.

The White House declined to comment on the WSJ report.

Pulte alleged in a post on X earlier on Wednesday that Cook had designated a condo in Atlanta as her primary residence after taking a loan on her home in Michigan, which she also declared as a primary residence. Pulte told CNBC he is also probing property Cook has in Massachusetts.

Loans for a primary residence can carry easier terms than those for second homes or investment properties.

Pulte asked US Attorney General Pam Bondi to investigate, and Trump quickly amplified the allegation.

Democrats on the US House of Representatives Committee on Financial Services blasted Trump's attack on Cook and vowed to fight it.

"Donald Trump is making up blatant lies in an effort to oust the first Black woman to serve on the Federal Reserve Board, so he can replace her with another unqualified loyalist who will do his bidding," they said in a post on X. "This is another attack on the Fed’s independence. We can’t let this happen."

Senator Elizabeth Warren, top Democrat on the Senate Banking Committee, echoed those concerns, saying in a statement: "The president and his administration should not weaponise the federal government to illegally fire independent Fed Board members." (Reuters)