Fannie Mae Chairman and Director of the Federal Housing Finance Agency Bill Pulte released a statement calling on Congress to investigate Powell. Pulte suggested that Powell should vacate his role at the Fed because of multibillion-dollar plans to renovate the Federal Reserve building and comments to Congress regarding the upgrades.

The president has been angry with Powell over the U.S. central bank's hesitance to succumb to his demand for lowering interest rates.

The Fed chief has repeatedly declined to say whether he will step down when his four-year term as chair expires in May, or remain on the Fed board.