The president’s about-face on the central bank chief, following advice from his treasury and commerce secretaries, sent markets surging.

WASHINGTON—President Trump said this week that he never had any plans to fire Federal Reserve Chair Jerome Powell, accusing the media of pushing a false narrative that he was out to get the central bank chief.

The president said he has “no intention” of ousting Jerome H. Powell, the Fed chair, but the administration’s willingness to challenge norms regarding the central bank’s political independence is causing concern.