Under the hard-won 2015 deal with Russian Federation, the US, China, France, Britain, Germany and the EU, Iran agreed to curb its nuclear programme in exchange for lifting of a raft of worldwide sanctions.
The landmark agreement signed between six world powers is officially known as the Joint Comprehensive Plan of Action.
Trump warned that he would scrap the agreement limiting Iran's nuclear program - an accord he has long despised - unless European countries "join with the United States in fixing significant flaws in the deal". He is seeking unilateral changes in the terms of the deal on the United States side and a radical re-negotiation on the part of the Iranians and Europeans, neither of which he is likely to get.
Under the deal, Iran undertakes to curb its nuclear activities and place them under total control of the International Atomic Energy Agency (IAEA) in exchange of abandonment of the sanctions imposed previously by the United Nations Security Council, the European Union and the United States over its nuclear program.
The president's proposals to "fix the deal's disastrous flaws" include Iran's agreement to open all sites immediately to worldwide inspectors and an assurance from Tehran that it never develop a nuclear weapon.
Washington also announced sanctions against 14 entities and people, including the head of Iran's judiciary, Ayatollah Sadeq Larijani. "We are also targeting Iran's ballistic missile program and destabilising activities, which it continues to prioritise over the economic well-being of the Iranian people".
The solidity of Iran and worldwide support for the agreement have blocked attempts by Trump and Israel to terminate this agreement or make changes to it, said the statement.
The administration official said the sanctions are part of a broader effort to counter Iran's "reckless" and "destabilizing behavior", including actions related to the crackdown on protesters, at least 21 of whom have been killed this month.
"I'm all in favor of trying to address the agreement's weaknesses", Representative Eliot Engel, a New York Democrat, said in a statement.
The sanctions with the most political repercussions are against the administrative head of Iran's judiciary, Sadegh Amoli Larijani.
Iranian Foreign Minister Mohammad Javad Zarif took to Twitter to describe Trump's decision and the announcement as "desperate attempts to undermine a solid multilateral agreement".
The Islamic Republic's foreign ministry said in a statement that it would not "move beyond its commitments" to the existing agreement, to which Trump has extended the USA commitment for another 120 days, Iran's state-run Islamic Republic News Agency (IRNA) reported on Saturday.
French President Emmanuel Macron phoned Mr Trump on Thursday to call for "the strict application of the deal and the importance of all the signatories to respect it".
On the streets of Tehran, many have grown cynical and exasperated by the endless pressure from the United States. USA and other officials have complained that Iran's ballistic-missile program can easily be converted for nuclear use. "Rather than repeating exhausted rhetoric, the USA must bring itself into full compiance - just like Iran", he said.
Trump said that any legislation regarding Iran must demand worldwide inspections when requested at all sites, must ensure Iran doesn't come close to possessing a nuclear weapon, must not have any expiration date and must state that long-range missile and nuclear weapons programs are inseparable.