They are enraged that the United States has effectively paralyzed the W.T.O. by refusing to sign off on new appointees to a crucial appeals panel. Without the panel, there is no way to enforce international trade rules and officially resolve disputes between members.

The two governments also remain at odds over plans by France, a European Union member, to tax American technology companies, and what each side believes are unfair subsidies that the other offers to an aircraft manufacturer, Airbus in Europe and Boeing in the United States.

“I can assure you we will be no shrinking violets,” Mr. Hogan said Thursday.

Mr. Hogan’s four-day visit got off to a promising start on Tuesday after he joined Robert Lighthizer, the United States trade representative, and their Japanese counterpart in signing an agreement to try to rein in what they said were unfair trade practices by China.

But his comments on Thursday morning, at an event hosted by the Center for Strategic and International Studies, a Washington think tank, suggested that deep tensions remained. Mr. Hogan, who became the European Union’s trade commissioner in December, appeared to be delivering on expectations that he would deploy his trademark bluntness to meet the Trump administration on its own terms.

“No other market is as free and open for U.S. businesses as the E.U. Where else are you as welcome?” Mr. Hogan said. “I might add I am coming under pressure to defend this level of openness given that our European businesses can be hit with unjustified tariffs and restrictions at a moment’s notice.”

He also quipped that Mr. Trump was guilty of “gloating” and accused him of reneging on an agreement that the United States and the European Union reached in July 2018 to negotiate a trade deal that excluded agriculture. Trump administration officials subsequently realized that a deal that did not address farm goods would meet opposition in Congress, and refused to proceed on those terms.

Mr. Hogan told reporters that he had been discussing various situations to overcome that impasse and suggested that the Americans and Europeans might consider the kind of “mini package” that the United States had negotiated with Japan and other countries. Instead of more broadly opening up agricultural markets, such a deal might focus on specific standards that American farmers often complain block their goods from European markets.