The decision was due by Friday, but the tariffs have provoked fierce opposition among industry leaders and in Congress. In addition, the White House is now engaged in preliminary trade talks with the European Union and with Japan, and auto tariffs would throw a bomb into those negotiations.

“Pleased that @POTUS has delayed decision on auto tariffs,” Senator Rob Portman, Republican of Ohio, tweeted Wednesday in response to media reports that the levies would not be imposed.

Auto tariffs would have opened another front to Mr. Trump’s trade war, but one with much smaller potential benefits and larger political liabilities. Auto industry executives on both sides of the Atlantic are opposed to tariffs, and the duties would have inflicted collateral damage on some of his most loyal voters in states like Alabama and South Carolina, which are home to big Mercedes-Benz and BMW factories.

“Our biggest market is Germany,” said Jeppe Kofod, a member of the European Parliament from Denmark. “The mere fact that Germany is hurt — we would be very much affected by that.”

The 25 percent tariff on steel and the 10 percent tariff on aluminum that the Trump administration imposed last year have had a more muted economic effect, but they have done much to rattle alliances.

Mexico and Canada, both of which retaliated with tariffs of their own, have previously appeared to be close to an agreement. But Mr. Trump has been hesitant to relent over his desire to protect America’s steel and aluminum sectors and his belief that the tariffs might be used as further leverage.

The United States and Canada sent mixed signals Wednesday about the future of the steel and aluminum tariffs. The Canadian foreign minister, Chrystia Freeland, declined to say whether the countries had struck a deal to lift those tariffs after meetings with lawmakers and Robert Lighthizer, the United States trade representative, in Washington on Wednesday.