Months of intense negotiations with the Europeans to keep the accord in place collapsed over Mr. Trump’s insistence that the limits placed by the agreement on Iran’s nuclear fuel production were inadequate. Under the provisions of the deal, those limits, or “sunset clauses,” were to expire in 2030 — 15 years after the deal was signed.

As a result, the United States will reinstate all the sanctions it had waived as part of the nuclear accord, and it will impose additional economic penalties that are now being drawn up by the Treasury Department.

Treasury Secretary Steven Mnuchin declined on Tuesday to specify what additional sanctions the United States might impose, but he expressed confidence that they would still be powerful even if other American allies did not follow suit.

“We do not want to let Iran use the U.S. financial markets and financial system and transact in dollars until they agree that not only will they not have a nuclear weapon now, but we’ve put in provisions that they will never have one,” Mr. Mnuchin said.

In his announcement, Mr. Trump recited familiar arguments against the deal: that it does not address the threat of Iran’s ballistic missiles or its malign behavior in the region, and that the expiration dates for the sunset clauses open the door to an Iranian nuclear bomb down the road.

Even if Iran was in compliance, he said, it could “still be on the verge of a nuclear breakout in just a short period of time.” In fact, under the deal, the limits on Iran’s uranium enrichment and stockpiles of nuclear fuel mean that Iran would not be on the verge of a nuclear breakout until 2030.

Still, Mr. Trump said, the United States and its allies could not stop Iran from building a nuclear weapon “under the decaying and rotten structure of the current agreement.”