But the president also promised to scrap the landmark agreement in 120 days if Congress and European allies don't meet his new demands for strengthening the deal - throwing down the gauntlet on a signature achievement of Barack Obama's presidency. The sanctions are an apparent American response to the recent wave of protests across Iran.
"If at any time I judge that such an agreement is not within reach, I will withdraw from the deal immediately", he added.
The president called for European allies to strike a deal fixing the terms of the worldwide agreement, which unfroze key Iranian financial assets in exchange for a reduction in its nuclear programs.
In a statement Saturday, Iran's Foreign Ministry said the Trump administration's "hostile and illegal act" in including Larijani on its sanctions list "has gone way beyond all internationally accepted behavior red lines".
Iran did not immediately react to the announcement, though officials said they were prepared if Trump had made a decision to act.
Officials from major world powers and Iran meet roughly every three to four months to assess implementation of the deal, which is monitored by the world's nuclear watchdog, the International Atomic Energy Agency.
White House officials played up the sanctions against Larijani as a symbol of Trump's displeasure with the Islamic Republic's government, and solidarity with those who are rallying against it.
"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.
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He (Ashley) knows he has to improve the team so that we have the quality which allows us to stay in the Premier League .
"I have been very clear about my opinion of that deal".
He paired Friday's concession with other, targeted sanctions on Iran for human rights abuses and ballistic missile development. But his explicit warning to Europe that the deal must be fixed by the time the next sanctions waivers are due in the spring creates a high-stakes diplomatic deadline that will be hard to meet.
The president charged that Iran has gotten "far too much in exchange for far too little", and threatened not to renew the waivers when the next approval period comes.
There is also no evidence that the Europeans have the appetite to reopen the deal.
Iran vowed on Saturday that it will retaliate against US President Donald Trump's decision to slap its judiciary head with sanctions.
He cited what he said were efforts by Tehran to obtain nuclear weapons, develop ballistic missiles, and support terrorist organizations, as well as what he called regional aggression, and "the cruel repression of Iranian citizens". There were images of a smiling Zarif, seated among smiling European officials, followed by a parade of statements in favor of the deal.
"Is he bluffing? I don't think so".
In particular, it will not begin to expire after 10 years as parts of the existing deal do, but instead would impose permanent restrictions on not just Iran's nuclear plants but also its missile programme. It is hard to imagine how Tehran would take European demands for changing the deal seriously when those players know the demands come under duress. "It is delivering on its main goal, which means keeping the Iranian nuclear program in check and under close surveillance".