Posting on his Truth Social platform on Friday, Trump called Powell "stubborn".
The Fed chair has been subjected to vicious verbal attacks by the Republican president over several months.
The Fed has the responsibility of stabilising prices and maximising employment.
Powell has held its benchmark rate for overnight loans constant this year, saying Fed officials needed to see what impact Trump's massive tariffs had on inflation.
If Powell doesn't "substantially" lower rates, Trump said, "THE BOARD SHOULD ASSUME CONTROL, AND DO WHAT EVERYONE KNOWS HAS TO BE DONE!"
Trump sees the rate cuts as leading to stronger growth and lower debt-servicing costs for the federal government and homebuyers.
The president argues there is virtually no inflation, even though the Fed's preferred measure is running at an annual rate of 2.6 per cent, slightly higher than the Fed's two per cent target.
Trump has called for slashing the Fed's benchmark rate by three percentage points, bringing it down dramatically from its current average of 4.33 per cent.
The risk is that a rate cut that large could cause more money to come into the economy than can be absorbed, possibly causing inflation to accelerate.
The Supreme Court suggested in a May ruling that Trump could not remove Powell for policy disagreements.
This led the White House to investigate whether the Fed chair could be fired for cause because of the cost overruns in its $US2.5 billion ($A3.9 billion) renovation projects.
Powell's term as chair ends in May 2026, at which point Trump can put his Senate-confirmed pick in the seat.
