Iran says the USA has "crossed a red line" by imposing sanctions on the head of its judiciary, Ayatollah Sadeq Amoli-Larijani.
Senior US administration officials told reporters Trump would work with Europeans on a follow-on deal to enshrine triggers that the Iranian government could not exceed related to ballistic missiles.
U.S. President Donald Trump on Friday delivered an ultimatum to Washington's European allies to fix the "terrible flaws" in the Iran nuclear deal, or he'll pull the U.S. out in a few months' time.
"Diplomacy Works, a pressure group founded by former US secretary of state John Kerry to defend the 2015 deal with Iran, known as the Joint Comprehensive Plan of Action, gave a biting evaluation of Trump's move, saying ". the president's plan includes bullying our allies into fundamentally altering the terms of a deal that they know is working for our mutual security and have publicly stated they have no interest in amending".
"So Trump now has issued explicit May deadline to Congress and Europeans: Fix Iran nuke deal or no more sanctions waivers", wrote Mark Dubowitz, head of the Foundation for Defense of Democracies.
Washington policy hawks hailed Trump's decision, which they said would concentrate minds in Europe, where leaders have urged the U.S. president not to sabotage a deal they see as a landmark diplomatic success.
"This is a last chance", Trump said, pushing for a separate agreement and saying the United States would not waive sanctions again to keep Iran in the pact without such an agreement.
"Despite my strong inclination, I have not yet withdrawn the United States from the Iran nuclear deal", he said in a statement.
The Republican leader grudgingly agreed to sign sanctions waivers, ensuring Washington will live up to its commitments for another 120 days, but he cautioned it would be 'for the last time'.
America's allies see the accord as the best way to thwart Iran's nuclear ambitions and a victory for multilateral diplomacy.
Russia's deputy foreign minister, Sergei Ryabkov, described Mr Trump's comments as "extremely negative".
Trump now will work with European partners on a follow-on agreement that enshrines certain triggers that the Iranian regime can not exceed related to ballistic missiles, said senior administration officials who briefed reporters on the decision.
"We are gradually coming to the conclusion that an internal decision by the USA to leave the (Joint Comprehensive Plan of Action) has already been made or is close to being made", Ryabkov said in an interview with Interfax news agency. Saturday's statement from Iran's foreign ministry further criticised new sanctions on 14 individuals announced by the US Treasury on Friday over human rights issues and Iran's missile programme.
By law, the administration must certify to Congress every 90 days whether Iran is complying with a 2015 agreement it signed with the global community to limit its nuclear program.
The 2015 deal, he said, "is not renegotiable".
He was prepared to back a modification to the existing deal if it were made permanent, one official said. The other parties to the agreement would have been unlikely to join the United States in reimposing sanctions.
Officials, congressional aides and outside administration advisers had said the president would probably extend the sanctions waivers, citing progress in the U.S. legislation.
Britain, France and Germany had called on Trump on Thursday to uphold the pact.