The Trump administration has tried to use the steel and aluminum tariffs as a bargaining chip to persuade other countries to voluntarily restrain their metal shipments to the United States or make other trade concessions. The administration may be looking to use the auto tariffs similarly, as leverage to force concessions from trading partners like Canada and Mexico.

“I think your autoworkers and your auto companies in this country are going to be very happy with what’s going to happen,” the president said on Wednesday afternoon as he prepared to board Marine One. “Nafta is very difficult. Mexico has been very difficult to deal with. Canada has been very difficult to deal with. They have been taking advantage of the United States for a long time. I am not happy with their requests. But I will tell you, in the end, we win.”

“Our autoworkers are going to be extremely happy,” he added.

In a Twitter post Wednesday morning, the president also hinted at the pending announcement.

“There will be big news coming soon for our great American Autoworkers,” Mr. Trump said. “After many decades of losing your jobs to other countries, you have waited long enough!”

But the proposal drew what appeared to be a swift backlash from the car industry. Some auto industry representatives said they worried that the plan could raise prices for cars and trucks in the United States, and end up leading to a less competitive American industry and fewer choices for American consumers.

“If these reports are true, it’s a bad day for American consumers,” said John Bozzella, the chief executive of Global Automakers, a trade group. “To our knowledge, no one is asking for this protection.”

In an April 2017 memo, the White House described several sectors as “critical elements of our manufacturing and defense industrial bases, which we must defend against unfair trade practices and other abuses.” That included vehicles, along with products like steel, aluminum, aircraft and semiconductors.