Even Washington’s closest ally, Britain, has openly split with those in the administration arguing to ditch the accord. At a news conference in London on Thursday with Secretary of State Rex W. Tillerson, Britain’s foreign minister, Boris Johnson, noted that “the North Korea crisis shows the importance of having arrangements such as the J.C.P.O.A.,” using the acronym for the formal name of the agreement, the Joint Comprehensive Plan of Action.

He called it “a position you and I have both adopted,” underscoring Mr. Tillerson’s now widely acknowledged disagreement with Mr. Trump over the importance of the deal.

Mr. Johnson added that in Iran, “a country of 80 million people, many of them young, potentially liberal, could be won over — could be won over to a new way of thinking.” He said that Iranians should see the economic benefits of the nuclear deal and that he had emphasized the point to Mr. Tillerson and other American officials.

Mr. Trump’s gradual movement on Iran has been seen as a bellwether of a foreign policy shift underway in the White House, especially since the ouster of Stephen K. Bannon, his former strategist. Mr. Bannon had made confrontation with China and Iran a central element of his approach to reasserting American pre-eminence around the world.

Two of the president’s remaining advisers, Lt. Gen. H. R. McMaster, his national security adviser, and Defense Secretary Jim Mattis, are known for hawkish views on Iran. But they do not bring to the debate a sense that the United States is engaged in a clash of civilizations against the country or its ideology. Instead, they have pressed for a quiet escalation of economic and military pushback against Tehran’s activities, including support for President Bashar al-Assad of Syria and terrorist groups as well as cyberattacks on American and Arab targets.

The Treasury Department did announce new economic sanctions on Thursday against individuals associated with Iran’s Islamic Revolutionary Guards Corps, the Quds Force, which is considered a channel to terrorist groups, and companies involved in hacking against American financial institutions in 2011 and 2012.

In announcing the new sanctions, a senior administration official, who insisted on anonymity while briefing a large group of reporters, said that over the past few years, the United States had focused too narrowly on nuclear issues and ignored Iran’s malign activities. But the administration made no mention of the 2016 indictment of seven Iranians for their involvement in that hacking.