Tehran has accused Washington of having "crossed all behavioral red lines of the worldwide community", by targeting judiciary chief Sadegh Amoli Larijani.
Issuing designations for 14 individuals and entities, Treasury Secretary Steven Mnuchin said the United States will not be a silent spectator while the Iranian regime continues to engage in human rights abuses and injustice.
Foreign Minister Mohammad Javad Zarif accused the U.S. of making a "desperate attempt" to undermine a "solid" deal.
Congress is split on the issue - hardline Republicans are urging the President to reimpose suspended sanctions and bring an end to the deal, while some liberal Democrats want to make it hard for Trump to withdraw from the deal without congressional consent.
"They should join us in constraining Iran's missile development and stopping its proliferation of missiles, especially to Yemen", he said.
Iran says its nuclear program is only for peaceful purposes.
Donald Trump's decision to target the judiciary head of Iran was not received well, Iran rejects Donal Trump's new sanctions for the nuclear deal and Iran spoke up guaranteeing a bitter response. "Here at the United Nations, we look forward to gaining new worldwide cooperation to strengthen actions against Iranian missile activity, enforce arms embargoes that Iran violates, crack down on Iranian sponsorship of terrorism, and continue to shine a light on Iranian human rights violations".
Iran has dismissed US calls for the quit of missile program development, and it has stressed that its nuclear program is peaceful.
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The EU said in a statemen t on Friday that it had taken note of Trump's decision and would assess its implications.
Although the USA has suspended sanctions against Iran following the nuclear deal, it still imposes punitive measures over issues such as terrorism, human rights and ballistic missile development.
Diplomacy Works, a pressure group set up by former secretary of state John Kerry to defend the deal, was scathing.
Russia, as well as the European Union, remains committed to the Iran nuclear deal, despite the recent U.S. waiver of sanctions against the country. JCPOA is not renegotiable: "rather than repeating exhausted rhetoric, U.S. must bring itself into full compliance -just like Iran".
In his statement Friday, Trump said he remained open to revising the Iran Nuclear Agreement Review Act, or INARA.
On Saturday, French President Emmanuel Macron stressed the "necessary respect by all parties" of Iran's nuclear deal with world powers, in a telephone call with Israeli Prime Minister Benjamin Netanyahu.
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.
The International Atomic Energy Agency has said Iran is complying with the terms of the deal, but Trump has long called the agreement "the worst deal ever".
But Trump argues that his predecessor Barack Obama gave away too much to Iran in sanctions relief, without forcing the Islamic republic to end its ballistic missile programme and support for militant groups.