But while Mr. Trump sees the car tariffs as leverage, the Europeans see them as a bomb that could shatter negotiations.

“If there ever were to be the unilateral imposition of tariffs, the talks would be ended,” David O’Sullivan, the departing European Union ambassador to the United States, said late last month.

The two sides are trying to move forward. Ms. Malmstrom met with Robert Lighthizer, the United States trade representative, on Wednesday, while Mr. Kudlow and Martin Selmayr, the European Commission’s secretary general, will convene on Thursday.

Mr. Trump technically has until mid-May to make a decision on the auto tariffs, though legal experts say he could continue to delay as long as talks continue. The Commerce Department, which has been studying the tariffs, sent a report with its findings to the White House on Feb. 17.

The details have not been made public, but a draft that circulated in early February determined that auto imports threatened the United States’ national security, according to one person who viewed it. Such a finding would pave the way for Mr. Trump to impose across-the-board tariffs. The report also presented other actions the president could take to stem imports, including trade barriers focused exclusively on autonomous vehicles and parts, according to several people familiar with the findings.

Mr. Trump had prioritized restarting trade talks with the Europeans as part of his global push to negotiate deals on his own terms. But as the president dangled the threat of tariffs last July, the Americans and the Europeans were not sure they could even reach an agreement to begin negotiating.

The night before the July 25 Rose Garden ceremony, Mr. Kudlow and Mr. Selmayr met over Diet Cokes at the Hay-Adams hotel near the White House. Mr. Kudlow had been encouraged by common interests between the United States and Europe, particularly a European offer to import large volumes of natural gas and soybeans.