BERLIN—German Chancellor Angela Merkel on Thursday threw her weight behind back-channel efforts to eliminate car import tariffs, fueling hope of a resolution aimed at heading off unilateral U.S. moves in the all-important sector.

Ms. Merkel’s comments bolstered German auto stocks, which soared 5% on Thursday after news of a meeting between the U.S. ambassador to Germany and the heads of the big three German auto makers—part of ongoing consultations on scrapping car tariffs altogether.

Any...