They can retreat in sullen bitterness, as one European official put it, but they realize that would accomplish little.

They can ask for exemptions to the sanctions that the administration has said will be applied to any European business that trades with both Iran and the United States. But they have been told, with humiliating clarity, that there will be no exemptions.

They can look for ways to preserve the deal by extending financing and other guarantees to European investment in Iran. But even if those mechanisms worked — and there is little belief that they would — the Europeans have not yet decided how far they are willing to go in antagonizing Trump.