The risk of escalation is high since Mr. Trump has promised even more tariffs. Taking aim at German car manufacturers, the president has started an investigation into automobile imports to determine whether they pose a national security concern, the same justification used for his metal tariffs.

The European counterattack on $3.2 billion of goods, a response to the administration's measures on steel and aluminum imports, adds another front to a trade war that has engulfed allies and adversaries around the world. China and Mexico have already retaliated with their own tariffs, and Canada, Japan and Turkey are readying similar offensives.

The European Union fought back on Friday against the Trump administration's tariffs, slapping penalties on an array of American products that target the president's political base, like bourbon, motorcycles and orange juice.

"You look at the European Union," the president told a crowd in Duluth, Minn., on Thursday. "They put up barriers so that we can't sell our farm products in. And yet they sell Mercedes and BMW, and the cars come in by the millions. And we hardly tax them at all."

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The United States is fighting from a position of strength, with the American economy on track for one of its strongest years in a decade. Europe doesn't have the same defenses. Growth in the region is slowing, and that weakness has been compounded by political turmoil in Italy and Germany, as well as Britain's decision to leave the European Union.

But in a trade war no sides are left unscathed. Although Mr. Trump has sought to exert pressure on other countries, the global nature of supply chains means the tit-for-tat tariffs are ricocheting in unexpected ways and may ultimately cost jobs in the United States. Sales of Mercedes S.U.V.s, made in Alabama by the German automaker Daimler, could be hit by the American trade dispute with China. The Swedish manufacturer Volvo faces rising prices on the imported steel it uses at its Mack Truck factory outside Allentown, Pa.

The path to reconciliation is shrouded in uncertainty, creating the potential for broader strain in the global economy. While the Trump administration has sought to use economic force to exert concessions, the successive drumbeat of attacks has left little time to negotiate. Formal trade talks between Brussels and Washington have broken down, although informal channels have remained open.

The European Commission, the European Union's administrative arm, applied its sanctions more than a week earlier than expected, in what analysts said was a show of strength.

"It's a signal that the E.U. is striking back and taking this seriously," said Holger Schmieding, chief economist at Berenberg Bank in London.

As Mr. Trump pursues a nationalistic agenda, leaders in Europe and elsewhere are eager to demonstrate that they will continue to dismantle barriers to commerce, with or without the United States. Cecilia Malmstrom, the European commissioner for trade, was in New Zealand on Thursday negotiating a free-trade pact with the government there, the latest in a series of treaties signed or in the works, including ones with Japan, Canada and Australia.

"We did everything we could to avoid this situation, but now we have no choice but to respond," Ms. Malmstrom said in a speech in Wellington, New Zealand. "The E.U. has a responsibility to stand up for open global trade."

The new slate of European tariffs focuses on products that tend to be manufactured in Republican strongholds: whiskey and playing cards from Kentucky, recreational boats from Florida and rice from Arkansas.

But trade wars don't play out that neatly. It's not easy to strike precise targets without collateral damage.

Take the Mack Truck factory in Pennsylvania. Mack may be a quintessential American brand, but it's owned by Volvo Group, which is based in this seaport on Sweden's southwestern coast.

The Mack plant uses specially treated steel imported from Europe. American substitutes are not readily available, if at all. That means the Allentown factory has to pay 25 percent more for some kinds of steel, putting it at a disadvantage with its competitors who manufacture in Mexico and can get the same high-quality steel without paying the Trump tariffs. At least for the moment, vehicles made in Mexico are not subject to tariffs when they are imported into the United States.

Billy Joel sang about Allentown as the city where "they're closing all the factories down." The Mack Truck factory, in the suburb of Lower Macungie Township, has been an exception. It is "packed with orders," said Martin Lundstedt, the chief executive of Volvo Group, a manufacturer of trucks, buses and heavy equipment that is separate from the company that makes Volvo cars.

But he worried that demand could slip if costs in the United States rose and the trade dispute triggered an economic slowdown. "Yes, it will affect us, and we need to live with it," Mr. Lundstedt said. "It could be that if you have production in the U.S. you are punished."

It's a similar concern for ABB, a supplier of heavy electrical equipment based in Zurich. ABB makes electrical transformers in South Boston, Va., and Crystal Springs, Miss.

"We use a very specific kind of steel," said Ulrich Spiesshofer, the chief executive of ABB. "The capacity and the number of players for that kind of steel is very limited. The steel that we import from other places is being punished."

Eventually the competitiveness of the United States plants could suffer, Mr. Spiesshofer said.

Daimler, the maker of Mercedes cars, has already been caught in the crossfire between the United States and China. The company issued a profit warning on Wednesday, in part blaming tit-for-tat tariffs for a slump in the sales of S.U.V.s, which are built in Tuscaloosa, Ala.

In retaliation for tariffs imposed by the United States on Chinese goods, China has threatened to increase penalties on American cars to 40 percent from 15 percent. That would hurt sales in the huge Chinese market by raising sticker prices for Mercedeses from Alabama as well as BMWs made in Spartanburg, S.C.

"Fewer than expected S.U.V. sales and higher than expected costs — not completely passed on to the customers — must be assumed because of increased import tariffs for U.S. vehicles into the Chinese market," Daimler said in a statement late Wednesday.

Last year, BMW exported about 80,000 vehicles to China, including its X5 S.U.V., from the Spartanburg plant, its largest factory in the world. BMW said in a statement on Thursday that it did not need to revise its outlook for profit because of trade tensions, but the company added that it "continues to observe international developments closely."

Shares of major German and American carmakers fell sharply Thursday on worries of a trade-related slowdown. Daimler shares closed off more than 4 percent in Frankfurt trading, and BMW shares slipped 3 percent.

If the trade conflict continues, companies could consider relocating assembly lines to other countries, leading to job losses in the United States. BMW already has factories in South Africa and China, among other countries.

Carmakers would not make such a decision lightly. Moving manufacturing is expensive and takes years to carry out. The German carmakers continue to hope that the conflict will blow over and perhaps even provide a catalyst for removing trade barriers with the United States.

Currently the United States charges a 2.5 percent levy on imported foreign cars while Europe imposes a tariff of 10 percent on cars from the United States. German automakers would be happy if tariffs fell to zero in both directions, though only as part of a broad trade pact, Eckehart Rotter, a spokesman for the German Association of the Automotive Industry, said Thursday.

Ironically, the tariffs could have a small — if somewhat short-lived — upside for Europe. Local steel and aluminum may eventually fall in price because producers in countries like Russia or Japan will divert supplies that otherwise would have gone to the United States, creating a glut in the market. That would be bad for steel producers but good for machinery makers and other companies that use a lot of steel, potentially giving them an edge over their American competitors in overseas markets.

But any benefits for Europe would be erased by a sizable disruption to global commerce. The biggest problem for companies, regardless of nationality, is that they don't know how much more the trade conflict will escalate. The uncertainty may already be gnawing on growth.

"For the first time we're hearing about decisions to postpone investment, postpone hiring, postpone making decisions," Jerome H. Powell, the chairman of the Federal Reserve, said during a panel discussion with other central bankers in Sintra, Portugal, on Wednesday. "That's a new thing."