Ford and GM shares both added about 1% after opening with declines on the day.
The White House has until May 18 to make a decision on whether it will add duties to imports of vehicles and auto parts. The president is considering tariffs as high as 25% on cars.
Trump sees auto tariffs as key leverage in trade negotiations with the European Union and Japan. But the E.U. has plans to retaliate with its own tariffs on up to $300 billion of U.S. goods.
Bloomberg first reported the auto tariffs delay.