U.S. President Donald Trump is floating potential tariff relief for auto companies while launching the process to impose levies on imports of semiconductors and pharmaceuticals, amid mounting uncertainty over the direction of his global trade war.

Speaking at the White House on Monday, Mr. Trump said auto manufacturers that source parts from Canada and Mexico “need a little bit of time” to reorganize supply chains to produce more in the United States. “I’m looking at something to help some of the car companies,” he said, without providing details.

The Trump administration on Friday exempted smartphones, tablets and other technology products and components from 125-per-cent tariffs on China. Over the weekend, Mr. Trump and Commerce Secretary Howard Lutnick said these imports would instead be covered by a separate, planned tariff on semiconductors.

Asked Monday about tariff exemptions for smartphones, the President said “there will be maybe things coming up” and that he has had discussions with Tim Cook, the chief executive of Apple.

“Look, I’m a very flexible person. I don’t change my mind, but I’m flexible. And you have to be, you can’t just have a wall,” Mr. Trump said. “I don’t want to hurt anybody.”

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On Monday, White House spokesman Kush Desai said that, under Mr. Trump’s orders, the Department of Commerce was moving forward with investigations of semiconductors and pharmaceuticals under Section 232 of the Trade Expansion Act of 1962.

The procedure allows the U.S. government to impose tariffs on national-security grounds and Mr. Trump has previously used it for his 25-per-cent levies on all imports of autos, steel and aluminum.

“President Trump has long been clear about the importance of reshoring manufacturing that is critical to our country’s national and economic security,” Mr. Desai wrote in an e-mail.

Notices in the Federal Register indicated that the investigation will start with a three-week public comment period that begins Wednesday.

Mr. Trump said he hoped pharmaceutical tariffs would force drug manufacturers out of other countries and into the U.S. “Pharmaceuticals, we’re going to do,” he said. “The higher the tariff, the faster they come.”

Since returning to office in January, Mr. Trump has rolled out a long suite of tariffs as the centrepiece of his economic policy. But he has repeatedly and abruptly rejigged the plan, granting exemptions at times while hiking levies at others, leaving trading partners and companies unsure what to expect.

On April 2, he unveiled high tariffs on nearly every country and territory in the world, including an uninhabited Antarctic archipelago primarily populated by penguins. After a week of stock market routs and a sell-off of U.S. government bonds, he suddenly dropped the individual levies on most countries and replaced them with a 10-per-cent universal tariff. Conversely, he cranked up the rate on China by adding 125-per-cent tariffs to a pre-existing 20-per-cent levy.

Earlier in the year, he went back and forth on tariffing Canada and Mexico before ultimately settling on a 10-per-cent rate for oil, gas and potash and 25 per cent for everything else, but exempting goods traded under the U.S.-Mexico-Canada Agreement. Canadian- and Mexican-made autos, steel and aluminum are still subject to the separate 25-per-cent tariff regardless of whether they trade under USMCA.

David Adams, head of Global Automakers of Canada, which represents Honda, Toyota and several other overseas brands, said in an interview that it is difficult to divine Mr. Trump’s intentions from the brief comments Monday.

But Mr. Adams said the 25-per-cent tariffs are a violation of USMCA, which Mr. Trump signed in his first term, so it would make sense to drop them.

Flavio Volpe, who leads the industry group representing Canadian auto-parts makers, said Mr. Trump appears to have realized how deeply integrated the U.S. auto sector is with other countries.

“It’s an acknowledgment of just how critical Canada, Mexico and probably China are to auto manufacturing,” Mr. Volpe said. “Whether he takes that and does anything positive with it, that’s where the milk gets in the coconut.”

Since Mr. Trump imposed the 25-per-cent tariffs on Canadian-assembled cars, Ontario has already seen two temporary auto-plant shutdowns – at Stellantis’s factory in Windsor and General Motors’ facility in Ingersoll – and thousands of layoffs.

So far, auto parts themselves have remained exempt from the tariffs, avoiding choking off supply chains to U.S. plants.

Linda Hasenfratz, executive chair of Guelph, Ont.-based auto-parts maker Linamar, told The Globe and Mail that it would cost billions to move factories to the U.S. to avoid tariffs. She said companies see tariffs as a temporary measure and not something to plan a manufacturing strategy around.

Pharmaceutical tariffs, meanwhile, would hammer Canadian drugmakers exporting mostly less expensive generic drugs to the U.S. American patients, who already pay some of the highest medication prices in the world, would also be affected.

Inu Manak, a trade expert at the Council on Foreign Relations think tank in Washington, said Mr. Trump’s efforts to use Section 232 on semiconductors and pharmaceuticals could be open to a court challenge.

The President and Mr. Lutnick appear to be suggesting that the levies will simply be imposed on an expedited timeline and might not wait for the results of the investigation, she said. “This is supposed to be a real investigation, and I don’t see them using it that way.”