WASHINGTON — President Trump and Chancellor Angela Merkel of Germany made no attempt on Friday to hide their disagreements over the future of the Iran nuclear deal and trade relations between the United States and Europe after a day of White House meetings that appeared to have produced no breakthroughs on major disputes.

Mr. Trump and Ms. Merkel, who have had a chilly relationship from the start, steered away from the kind of awkward confrontations that have characterized past meetings, going out of their way to compliment each other and accentuate areas of agreement. But Mr. Trump pressed his complaint that the trade relationship between the United States and Europe was “unfair,” and Ms. Merkel made clear that the president had not made the commitment she was seeking — permanently exempting the European Union from the steel and aluminum tariffs he imposed in March.

“We need a reciprocal relationship, which we don’t have,” Mr. Trump said, standing beside Ms. Merkel at a news conference in the ornate East Room of the White House. “The chancellor and I have discussed it today at length, and we’re working on it. And we want to make it more fair and the chancellor wants to make it more fair.”

Ms. Merkel, alternating between looking serious and perplexed as Mr. Trump spoke, said he had given her no preview of what he might decide regarding the tariffs.