Iran also refused to accept any changes to its 2015 nuclear deal with the world powers.
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.
The 2015 nuclear accord, reached after months of painstaking negotiations with the U.S., Britain, France, Germany, China and Russian Federation, lifted worldwide sanctions in exchange for Iran limiting its nuclear program.
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".
Senior U.S. 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.
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Responding to Trump's harsh stance, Iranian Foreign Minister Mohammad Javad Zarif said on Friday that it was "desperate attempts" to undermine an accord which Iran said was "not renegotiable".
"JCPOA is not renegotiable: rather than repeating exhausted rhetoric, U.S. must bring itself into full compliance - just like Iran", Zarif tweeted immediately after Trump's speech.
The sanctions Trump waived Friday dealt with Iran's central bank.
Trump said that his decision will give Tehran and America's European allies time to fix the deal's "terrible flaws". "Instead, I have outlined two possible paths forward: either fix the deal's disastrous flaws, or the United States will withdraw".
Here's why this keeps coming up: Every few months - the terms vary - the president faces deadlines for deciding whether to continue waiving sanctions that Congress imposed years ago.
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Iran will definitely respond to the USA act by putting the name of Ayatollah Sadeq Amoli Larijani on list of sanctions.
A decision to withhold a waiver would have effectively ended the deal between Iran and the other global signatories.
A statement from J Street President Jeremy Ben-Ami called on members of congress and "any responsible officials remaining inside the administration" to take steps "to reverse this decision and prevent this disastrous policy from being carried out".
But to some in Washington, the meeting amounted to a show of unity between Europe and Iran - and of defiance toward the United States.
"Like it or not, we need to uphold our end of the bargain so that we can hold Iran to its obligations and crack down on the regime's other destabilizing activities".
Larijani is the most prominent of several Iranian officials and entities blacklisted, a roster of 14 individuals and entities that also includes the cyber unit of the Islamic Revolutionary Guard Corps, which the United States said has repressed social media networks that protesters can use to share information.
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