Less than two months on, frustration with the deal is growing in Europe. Businesses are halting exports to the U.S., complaining about new bureaucratic hurdles and warning about a new era of unpredictability.

The reason: the Trump administration’s decision to expand its 50% metals tariffs to cover hundreds of additional products that contain steel and aluminum, slapping a large number of European manufacturers with tariffs higher than the 15% Trump and the EU agreed on for most products.

While the U.S. steel and aluminum tariffs initially targeted only the metals themselves and mostly metal parts, such as screws, they now apply to such objects as motors, pumps, machine tools and construction equipment.

“About 30% of U.S. machinery imports from the EU are now subject to 50% tariffs on the metal content of the product,” Bertram Kawlath, president of the German Mechanical Engineering Industry Association, or VDMA, wrote in a letter to European Commission President Ursula von der Leyen at the end of August. The sector, he added, is facing an “existential crisis.”

The White House and the Department of Commerce didn’t immediately respond to requests for comment.

The grudging acceptance that greeted the July deal is now threatening to unravel. Discontent is spreading not just among politicians within EU member states but also to the European Parliament, whose approval is required for key parts of the deal to take effect.

“There is no security and predictability” in the U.S.-EU deal, said Bernd Lange, a German politician who leads the parliament’s trade committee. Lange said he now expects lawmakers to demand changes to draft legislation that would eliminate or reduce tariffs for a range of U.S. imports under the July agreement.

Why should the EU “give zero tariffs for U.S. motorbikes, knowing that now European producers have to pay not only 15% but also the steel and aluminum tariffs?” Lange said.

After the Department of Commerce expanded the metals tariffs to hundreds of derivative products starting last month, the company stopped exports to the U.S., halted production destined for the market and sent 100 workers home. Krone is looking into diverting shipments already under way to Mexico and Canada.

“We don’t know if our customers are ready to pay 15% or 50% more for a machine or its spare parts,” said Krone, adding that the disruption would affect the company’s U.S. sales for a long time.

Bernd Lange, a German politician, says there is ‘no security and predictability’ in the U.S.-EU deal.

U.S. companies are affected, too. John Deere, one of Krone’s largest competitors, has plants in Mannheim and Zweibrücken in Germany. About 20% of its German production is exported to the U.S., according to a company spokeswoman.

“We are relying on structural cost discipline and close cooperation with our distribution partners to cushion the impact” of the steel tariffs, the spokeswoman said. “We aren’t planning to relocate our production from Germany to the U.S.”

The effective tariff facing exporters now varies depending on a product’s metal content. For a machine worth $1 million with a 20% steel content, the rate would be 50% of $200,000 and 15% of the rest, resulting in a $220,000 levy per machine—or a 22% tariff. The U.S. has said it would review the metals tariff list every four months, adding to the uncertainty.

The VDMA is now demanding that the European Commission, which negotiated the deal on behalf of EU members, secure a 15% tariff cap on machinery, as it did for autos, semiconductors, pharmaceuticals and lumber.

EU trade chief Maroš Šefčovič said Wednesday that the EU doesn’t pose a threat to American steel producers, and both economies are dealing with cheap imports from other countries.

“I know that they understand the issue, they know about our positions, but when we will be able to resolve it I wouldn’t dare to say,” Šefčovič said.

European officials said after the trade deal was announced that the two sides would work on a quota system that could allow a certain volume of EU steel and aluminum into the U.S. at a lower tariff rate. But they haven’t disclosed any progress on those talks.

The VDMA says such quotas wouldn’t address the main complaint about the expanded steel tariffs: the bureaucratic burden they impose on manufacturers. If their products are on the steel tariff list, they need to research their metal content or risk penalties.

Krone says it must now document the steel and aluminum content of the 15,000 parts that make up its Big X forage harvester, for instance. Between 10% and 15% of the company’s farming-equipment sales go to North America.

Even companies whose products aren’t subject to the steel tariffs can get ensnared.

Take valves, a commodity device to regulate the flow of liquid in a machine. Valves aren’t on the expanded steel tariff list but are used in injection molding machines. Since these machines are on the list, their manufacturers must now obtain from their suppliers information about the steel content of their valves—where it was bought, at what price, and where the metal was melted and poured.

Unlike carmakers, machine makers are often small and midsize companies that don’t have much manufacturing capacity in the U.S.

Krone is planning to build its first assembly line near its U.S. headquarters in Olive Branch, Miss., but only for small machines. A dearth of skilled labor and high production costs make it harder to manufacture bigger, more complex equipment there, according to the company.

Andrew Adair, trade adviser for America at the VDMA, said American manufacturers in the U.S. could be among the first to suffer because they rely on imported machines that will now be more expensive, if they are available at all.

Vice President JD Vance held a speech at a plastics factory in Michigan in March, saying the Trump administration would “make it easier and more affordable to make things again in the United States.”

“Then they walked the factory floor,” said Adair. “And we had our experts look at the equipment: Virtually none of it was American-made. Most of it was imported.”

Write to Bertrand Benoit at bertrand.benoit@wsj.com and Kim Mackrael at kim.mackrael@wsj.com