"I am telling those in the White House that if they do not live up to their commitments, the Iranian government will react firmly," Rouhani said in a speech broadcast live on state television.
"If anyone betrays the deal, they should know that they would face severe consequences," he added.
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Rohani's remarks come as French President Emmanuel Macron is in Washington for talks likely to be dominated by the nuclear accord with Iran. Macron said on Sunday there was no “Plan B” for keeping a lid on Tehran’s nuclear ambitions.
He is on something of a rescue mission for what is formally known as the Joint Comprehensive Plan of Action (JCPOA), which Trump has said he will scrap unless European allies fix what he called “terrible flaws” by mid-May.
Iranian Foreign Minister Mohammad Javad Zarif called on European leaders to support it.
“It is either all or nothing. European leaders should encourage Trump not just to stay in the nuclear deal, but more important to begin implementing his part of the bargain in good faith,” Zarif wrote on his Twitter account.
The deal reached between six powers - all of whom but Germany are nuclear-armed - and Tehran put curbs on Iran’s nuclear program in exchange for sanctions relief.
Macron said on Fox News Sunday that it would be better to protect the deal instead of to get rid of it as there was no other plan.
“Is this agreement perfect and this JCPOA a perfect thing for our relationship with Iran? No. But for nuclear — what do you have? As a better option? I don’t see it,” he said.