WASHINGTON—Automakers will get a one-month reprieve from tariffs on Mexico and Canada for cars that comply with a free-trade agreement between those two nations and the U.S., the White House said Wednesday.

Prime Minister Justin Trudeau and his U.S. counterpart spoke by phone Wednesday about the ongoing trade war and their senior officials have been in constant contact throughout the day as both sides discuss possible tariff carve-outs for certain sectors.