Trump said he wanted America's European allies to use the 120-day period before sanctions relief again came up for renewal to agree to tougher measures and new conditions, otherwise Washington would pull out of the deal.
President kept the Iranian nuclear deal in place Friday for another 120 days but warned it's the last time, as the USA seeks a tougher agreement against Tehran with European allies, and the administration slapped with fresh sanctions unrelated to the agreement.
It also said Iran would not allow the deal to be linked to other issues, after Mr Trump suggested that the sanctions relief under the deal be tied to Iran limiting its long-range ballistic missile program.
"In what we heard Friday, I don't see any invitation for Iran to enter dialogue", he said.
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Trump had faced a Friday deadline to decide on whether to waive the sanctions. It is also wants to address Iran's ballistic missile programme. The last time he had to make a decision on the subject was in October - at the time, he gave a speech denouncing the deal, but left the final decision on re-imposing sanctions to Congress.
Iranian Foreign Minister Mohammad Javad Zarif responded, saying that the deal is not renegotiable and that Trump's stance amounts to "desperate attempts to undermine a solid multilateral agreement". Would you rather deal with those things with Iran having nuclear weapons or not having them?
Unrelated to the nuclear deal, Trump approved sanctions against 14 individuals and entities, including against Sadeq Larijani, the head of Iran's judiciary whom the Trump administration holds responsible for the violent crackdown on recent anti-government protests that erupted in the country.
In a telephone conversation with Trump on Thursday, French President Emmanuel Macron reiterated "the determination of France to support the strict implementation of the 2015 Iran nuclear agreement and the importance of it being respected by all signatories", said the Elysee Palace.
Two senior Trump administration officials told Reuters on Wednesday that the president, a Republican, had privately expressed reluctance to heed the advice of top advisers recommending he not reimpose the suspended sanctions.
Trump had certified the deal twice before, and senior officials have grudgingly said Iran is complying.