Most of the new duties kicked in Thursday, hitting countries with elevated rates that mark a departure from long-standing trade norms.

Olu Sonola, the head of U.S. economic research at Fitch Ratings, said the economy was just “starting to see” the effects of the tariffs that Mr. Trump announced in the spring, adding that with Mr. Trump’s newest duties now in place, Americans would “see that magnified” in coming months.