“Tariffs are the greatest!” the president wrote on Twitter on Tuesday. “Either a country which has treated the United States unfairly on Trade negotiates a fair deal, or it gets hit with Tariffs. It’s as simple as that - and everybody’s talking! Remember, we are the ‘piggy bank’ that’s being robbed. All will be Great!”

“The European Union is coming to Washington tomorrow to negotiate a deal on Trade,” he wrote later in another tweet. “I have an idea for them. Both the U.S. and the E.U. drop all Tariffs, Barriers and Subsidies! That would finally be called Free Market and Fair Trade! Hope they do it, we are ready - but they won’t!”

In a briefing on Tuesday, a senior European official denied that the tariffs had made the bloc more willing to negotiate. But the official said the Europeans were eager to find a course of action that could release both sides from a “downward spiral” of tariffs and retaliation.

But he added that the Europeans had not yet received a clear indication of the Americans’ primary goal, whether it was slashing tariffs on automobiles or reducing the United States trade deficit with Europe. He said people were struggling to understand the administration’s negotiation strategy, and whether it would change its approach from one day to the next.

During his visit, Mr. Juncker is prepared to discuss two options for the trading relationship, the official said, both of which the Europeans have floated with the United States before. The first is an agreement that would have all major global auto exporters slash their tariffs on foreign cars. The second calls for a limited trade deal between Europe and the United States centered on industrial goods.