BRUSSELS—U. S. President Donald Trump’s decision to extend tariff waivers on steel and aluminum imports for certain countries keeps a negotiating window open but doesn’t eliminate the risk of a trade war between America and its biggest economic partner, the European Union.

The White House is asking U.S. trade partners to agree to quotas in exchange for tariff waivers, effectively forcing them to concede to export curbs to safeguard broader trade links. The EU, however, has resisted voluntary restrictions as a violation of World Trade Organization rules.

Brussels and Washington have been on a collision course over Mr. Trump’s tariffs since March 23, when the measures and temporary exemptions—including for the EU—went into effect. In a sign of tough negotiations ahead, the EU’s executive arm, the European Commission, said Tuesday in an unenthusiastic statement that the bloc “takes note” of Mr. Trump’s last-minute postponement of his decision on the waivers by one month.

“The U.S. decision prolongs market uncertainty, which is already affecting business decisions,” the commission said. “The EU should be fully and permanently exempted from these measures.”

The EU-U.S. dispute threatens $1 trillion of annual trade in goods and services between the world’s two biggest markets. It also threatens to undermine efforts by Washington and Brussels to jointly counter China’s model of state capitalism, which Western officials say thrives on WTO loopholes.