President Donald Trump proposed to executives from the world’s biggest auto makers Friday imposing a 20% tariff on vehicles brought into the U.S. and also subjecting imports to tougher emissions standards than domestic vehicles, according to people familiar with the session.

During a tense meeting at the White House that was billed as a discussion of U.S. auto-emissions standards, Mr. Trump brought up the issue of trade and targeted European auto makers for not building more vehicles in the U.S., according to the people briefed...