But he says this waiver will be the last and is meant to secure an agreement from European allies to fix what he says are flaws in the pact.
Hardliners on Iran in the US Congress have called for the reimposition of the suspended sanctions and an end to the nuclear deal, while some liberal Democrats want to pass legislation that would make it harder for Trump to pull Washington out without congressional consent.
The Trump administration's sanctions also are intended at hindering Iran's ballistic missile program and other alleged "illicit activities".
What are the new sanctions?
The US Treasury issued a statement on Friday saying Ayatollah Amoli-Larijani was responsible for the "torture or cruel, inhumane, and degrading treatment or punishment of prisoners in Iran, including amputations". The sanctions, when they are in place, target third parties overseas that deal with Iran and have the effect - because of the reach of the USA dollar - of severely inhibiting trade with Iran.
It said the sanctions are against global law and go against USA commitments, saying they would bring a "strong reaction" from Iran.
It added that Trump had continued to "take hostile measures against the Iranian people and repeating the threats that have failed many times".
Mr Trump maintains that Iran is not complying with the spirit of the deal, despite his own advisors previously admitting there had been no technical violations.
In October, Trump decertified the nuclear deal under US law, saying the sanctions relief was disproportionate to Iran's nuclear concessions, and describing the arrangement as contrary to America's national security interests.
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That possibility is likely to be a big deal if the world tries to call Trump's bluff on the four month ultimatum, as he's always been inclined to kill the deal, but would look foolish if he tried to kill the deal only to have it continue without U.S. involvement, effectively removing the USA from the nations involved in enforcement of the terms.
In return, decades of worldwide and U.S. nuclear-related sanctions were suspended.
Under the terms of the landmark agreement the United States president must certify the deal every 90 days and pass sanction waivers every 120 days.
What does Mr Trump want to change?
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 next deadline to waive sanctions under the agreement is the middle of May. Instead, I have outlined two possible paths forward: "either fix the deal's disastrous flaws, or the United States will withdraw", read a statement.
"They should join us in constraining Iran's missile development and stopping its proliferation of missiles, especially to Yemen", he said.
"We know the European Union and other powers want to keep the nuclear deal, nearly no matter what", David Pollock, a senior fellow at the Washington Institute for Near East Policy, told Xinhua.
What have other countries said? "It's going to be complicated to save the deal after this", said one European diplomat, speaking on condition of anonymity.