President Trump stepped up his pressure on the Federal Reserve to lower borrowing costs on Monday, accusing its chair, Jerome H. Powell, in a handwritten note of costing the country “a fortune” and demanding that he cut interest rates “by a lot.”

In a separate social media post on Monday, Mr. Trump said Mr. Powell and his colleagues on the Fed’s Board of Governors, who vote on every monetary policy decision, “should be ashamed of themselves for allowing this to happen to the United States.”

“If they were doing their job properly, our Country would be saving Trillions of Dollars in Interest Cost,” Mr. Trump wrote. “The Board just sits there and watches, so they are equally to blame.”

The criticism is the latest in months of attacks in which Mr. Trump has insulted Mr. Powell directly and has even threatened to fire him as chair. On Friday, the president encouraged Mr. Powell to resign before his term as chair is up in May. Mr. Powell can stay on as a governor until 2028 if he chooses.

Mr. Trump has also floated naming a replacement for Mr. Powell before his term expires, a move that could complicate communications for the Fed.

The next opening on the Fed board is for the slot occupied by Adriana Kugler, whose term is set to expire in January. On Monday, Treasury Secretary Scott Bessent floated the idea of appointing Mr. Powell’s successor to that position and later elevating that person to be chair.