Three former heads of the US central bank have decried federal prosecutors' criminal investigation into chair Jerome Powell as an "unprecedented" bid to undermine the Federal Reserve's independence.

In a statement on Monday, 10 economic policy leaders - including former Treasury Department secretaries - joined former Fed chairs Janet Yellen, Ben Bernanke and Alan Greenspan to rally behind Powell.

"The Federal Reserve's independence and the public's perception of that independence are critical for economic performance," they wrote.

The probe, they added, "has no place in the United States whose greatest strength is the rule of law, which is at the foundation of our economic success".

"This is how monetary policy is made in emerging markets with weak institutions, with highly negative consequences for inflation and the functioning of their economies more broadly," the former economic policy leaders said.