Mr. Trump has frequently championed the company as a success story in domestic manufacturing. Soon after taking office in 2017, Mr. Trump hosted Harley-Davidson executives at the White House, where he called the firm a “true American icon” and thanked it “for building things in America.”

Like many American companies, Harley-Davidson has increasingly relied on overseas markets for sales and has shifted some production as a result. The company now produces some bikes and parts at facilities in Brazil, Australia, India and Thailand, and has shifted production to India and Thailand specifically to avoid high import tariffs in those countries. The company sold about 40,000 new motorbikes last year in Europe, equivalent to a sixth of its worldwide sales, making the region its most important market after the United States.

[Read more: Even Harley-Davidson can’t avoid the tug of overseas factories.]

Harley-Davidson did not specify how many jobs it might shift to its overseas facilities as it ratchets up European production, and a spokesman for the company said it was “still evaluating” the need for job cuts in the United States. The company has been consolidating its United States operations, eliminating hundreds of jobs in the process.

Shares of Harley-Davidson fell nearly 6 percent in afternoon trading.

Moving production abroad could draw the ire of Mr. Trump, who as a presidential candidate publicly assailed companies such as the furnace and air-conditioner maker Carrier, which planned to close a plant in the United States and shift manufacturing operations to Mexico. Mr. Trump regularly tells his supporters that American manufacturing is making a comeback and lavishes praise on companies that build domestically.

But that was before Mr. Trump followed through on his plans to impose tariffs on foreign steel and aluminum, a move he says will force other countries to lower their trade barriers. So far, the opposite has happened, as the European Union, Mexico and Canada respond with their own levies, many of which are aimed at products from politically important states that supported Mr. Trump, like Ohio, Iowa, Pennsylvania and Wisconsin.

Speaker Paul D. Ryan, a Wisconsin Republican, said on Monday that Harley-Davidson’s decision was evidence that raising trade barriers was a bad idea.

“This is further proof of the harm from unilateral tariffs,” Mr. Ryan said. “The best way to help American workers, consumers and manufacturers is to open new markets for them, not to raise barriers to our own market.”