American allies have already been told by US officials that they should be prepared to join in reopening negotiations with Iran, or expect that the United States may abandon the agreement, as it did the Paris climate accord.

The United States has begun raising the possibility of demanding access to military sites in Iran where there is reasonable suspicion of nuclear research or development with international inspectors in Vienna, according to several foreign officials.

Rufusal by the Iranians could enable Washington to declare Tehran as being in violation of the deal.

Because it was never a treaty, Trump has latitude to abandon the accord. President Barack Obama made an executive agreement, which his successor can eliminate by disregarding the accord’s requirement to waive sanctions against Iran.

Trump’s instructions followed a series of exchanges with Secretary of State Rex W. Tillerson, after Trump balked at certifying for a second time since he took office, that Iran is in compliance with the agreement. He later reluctantly approved the certification.

According to an official, regarding his inability to find Iran non-compliant, “he had a bit of a meltdown when that wasn’t one of the choices.” He’s made it clear he does not plan to let that happen again.“We’re doing very detailed studies,” he told The Wall Street Journal in an interview this week. He later said that when the next 90-day review of the deal comes around, “I think they’ll be noncompliant.”

His aides described the studies Mr. Trump referred to as evenhanded efforts to evaluate the costs and benefits of staying inside the deal, which limits Iran’s ability to produce nuclear fuel for at least the next nine years, versus abandoning it.

Some say that abandoning the agreement would come at a high diplomatic cost. Britain, China, France, Germany and Russia, the other parties to the agreement, do not share Mr. Trump’s objections. The United States will be isolated on the issue, if it withdraws support for the accord, much as it is on the climate change agreement.

Still, Trump said, “Look, I have a lot of respect for Rex and his people, good relationship,” he said of Mr. Tillerson. “It’s easier to say they comply. It’s a lot easier. But it’s the wrong thing. They don’t comply.”

In an interview this week with The Washington Post, the chairman of the Senate Foreign Relations Committee, Bob Corker, Republican of Tennessee, and longtime critic of the deal, suggested that this is not the moment to abandon something that is largely working. “What I say to the president, and this is what Tillerson, Mattis and McMaster say,” said Mr. Corker, referring to Defense Secretary Jim Mattis and the national security adviser, Lt. Gen. H. R. McMaster, is that “you can only tear the agreement up one time.” He argued for a more nuanced approach. “Radically enforce it,” and demand access to “various facilities in Iran.”