Despite Iranian denials, inspections were a topic of discussion at the negotiations in Switzerland over the weekend, two officials familiar with the talks said. The idea under consideration would grant the International Atomic Energy Agency, the U.N.’s nuclear inspection arm, broad powers to inspect just about any suspect site on short notice. It revives ideas that were being discussed in February, in Geneva, when the Iranians and the Americans were meeting Jared Kushner, the president’s son-in-law, and Steve Witkoff, his special envoy, before the negotiations broke off when Mr. Trump ordered the attack on Iran.

At the Swiss resort this past weekend, the secretary general of the I.A.E.A., Rafael Mariano Grossi, was in the hallways and negotiating rooms talking to each side, describing what kind of access his inspection teams would need to assure no nuclear fuel was being diverted to weapons projects, according to diplomats who were familiar with the discussions. The Iranians appeared to agree to the concept, but did not want to agree to dates or details until other parts of the accord — including when they would have access to billions of dollars in frozen funds — were worked out.

So when Mr. Vance declared on Monday that Tehran had agreed to allow I.A.E.A. inspectors into the sites, calling it “the first step” toward ensuring that Iran did not obtain a nuclear weapon, Iran’s Foreign Ministry spokesman, Esmail Baghaei, immediately pushed back, saying that there were no plans to allow inspectors access to facilities at Isfahan, Natanz and Fordo, all of which the United States bombed a year ago. And, in fact, there is no imminent plan.

That prompted Mr. Trump to say on Tuesday that if there were no inspections, there was no accord. Secretary of State Marco Rubio was a little more careful.

“I don’t know why they have to say the things they say,” Mr. Rubio told reporters in Abu Dhabi, where he was beginning a tour of the Gulf states, trying to drum up support for the deal with Iran. He noted the complexity of Iran’s internal politics and said: “I guess they’ll navigate it. But we know what they agreed to do, and now they’ll either do it or they won’t.” Mr. Trump, he said, “will have some decisions to make.”