The European pharmaceutical industry is pushing for the United States to recognize clinical trials of new drugs conducted in Europe and vice versa. That would cut the cost of testing a new drug by millions of dollars and help hold down prices for prescription medicines.

Brussels trade negotiators hope that “as long as there is constructive work toward a stronger future trade relationship, the United States will withhold the urge to impose further tariffs,” said Koen Berden, a trade expert at the European Federation of Pharmaceutical Industries and Associations.

“They to want to show to Trump that we are serious and we want this to work,” Mr. Berden said in an interview Monday.

But the proposals under discussion fall well short of the “new phase in the relationship between the United States and the European Union” that Mr. Trump and Jean-Claude Juncker, the president of the European Commission, described after a meeting at the White House in July.

The meeting in Washington on Wednesday will be the second between Mr. Lighthizer and Ms. Malmstrom since July, and her first trip to Washington. Members of their staffs have met more frequently. They have focused on regulations, which are often a more serious impediment to trade than tariffs.

As for the trade deficits, most economists do not see any gap as money “lost” to other countries and do not agree with the president’s view that the trade imbalance shows America’s weakness on trade policy.

On Sunday, President Emmanuel Macron of France criticized Mr. Trump’s nationalistic posture in his remarks at the commemorative event at the Arc de Triomphe in Paris.