WASHINGTON — President Trump said on Saturday that he had the power to remove or demote Jerome H. Powell, the Federal Reserve chair, renewing a long-running threat against the central bank’s leader at a time when it could further roil volatile markets.

Mr. Trump said in a news conference at the White House that ousting Mr. Powell was not his current plan but that he was “not happy with the Fed” because it was “following” and “we should be leading.” He said he had the right to remove Mr. Powell as chair “and put him in a regular position and put somebody else in charge,” but added, “I haven’t made any decisions on that.”

While it was a familiar threat from a president who has continually beaten up on Mr. Powell, it was made in the midst of growing concern that the spread of the coronavirus could tip the United States into a recession.