Trump's decision avoided placing the United States in violation of the commitments it made in the landmark 2015 deal. But he affirmed his willingness to withdraw from it in a few months unless changes are made.
"Despite my strong inclination, I have not yet withdrawn the United States from the Iran nuclear deal," Trump said in a statement. "Instead, I have outlined two possible paths forward: either fix the deal's disastrous flaws, or the United States will withdraw."
Critics of the deal deemed the president's decision "an opportunity to do better," as Sen. Bob Corker (R-Tenn.), chairman of the Senate Foreign Relations Committee, called it.
But supporters expressed skepticism that the deal will survive in its current form. Trita Parsi, head of the National Iranian American Council, called it a "temporary stay of execution."
"In a nutshell, he's saying, 'Kill the deal with me, or we'll kill it alone,' " said Robert Malley, who worked on the National Security Council under President Barack Obama.
Trump blamed Iran for a litany of alleged malign activities, including support for terrorist groups and the "murderous regime" of Syrian President Bashar al-Assad, and torture, mass arrests and oppression at home.
Trump said his strategy for confronting Iran through sanctions and support for Iranian political freedom "stands in stark contrast to the policy and actions of the previous administration."
"President Obama failed to act as the Iranian people took to the streets in 2009. He turned a blind eye as Iran built and tested dangerous missiles and exported terror. He curried favor with the Iranian regime in order to push through the disastrously flawed Iran nuclear deal," he said.
Iranian officials warned that a U.S. withdrawal from the deal would spell its doom.
Foreign Minister Mohammad Javad Zarif said on Twitter that "Trump's policy & today's announcement amount to desperate attempts to undermine a solid multilateral agreement."
"JCPOA is not renegotiable," he said, using an abbreviation for the deal's formal name, the Joint Comprehensive Plan of Action. "Rather than repeating tired rhetoric, US must bring itself into full compliance — just like Iran."
As a signatory to the international Non-Proliferation Treaty, Iran has committed to not building nuclear weapons, even after the restrictions on its program lapse, and it is entitled to use nuclear technology for peaceful purposes.
Trump listed his conditions for legislation that would address future U.S. participation and called on European allies "to join with the United States in fixing significant flaws in the deal, countering Iranian aggression, and supporting the Iranian people."
"If other nations fail to act during this time, I will terminate our deal with Iran," warned Trump, who will revisit the decision in 120 days.
Officials said the administration will discuss the changes it is seeking with Europeans but will not talk directly with Iran.
Sen. Benjamin L. Cardin (Md.), the top Democrat on the Senate Foreign Relations Committee, called Trump's statement an "ultimatum" and said the president is "making negotiations with Europe more difficult by the way he's laying out the conditions."
All parties to the accord would have to agree to any changes. That is highly unlikely. The Europeans, who consider the deal a great success contributing to their security, have said that Iran's non-nuclear behavior must be addressed separately.
The changes Trump has demanded include timely inspections of all sites requested by the International Atomic Energy Agency, reflecting a concern that Iran could be conducting nuclear research clandestinely at military sites.
Trump also wants to terminate the phased expiration dates of various limitations placed on Iran's nuclear program. Sometimes called "sunset provisions," many of them lapse 10 to 15 years in the future. Trump wants them to continue indefinitely so that the United States can rapidly resume sanctions if Iran is ever found to be cheating.
Rep. Eliot L. Engel (N.Y.), the top Democrat on the House Foreign Affairs Committee, said the demands are unattainable.
"The Trump administration's policy announced today sets impossible standards that would ultimately isolate the United States rather than isolating the regime in Tehran," he said.
"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."
Some of the new sanctions announced by the Treasury Department are a response to crackdowns on anti-government protests and blocking access to social media sites.
The entities sanctioned include Iran's Supreme Council of Cyberspace and its subsidiary, the National Cyberspace Center, which police the Internet, restricting access to websites that challenge the regime.
The sanctions with the most political repercussions are against the administrative head of Iran's judiciary, Sadegh Amoli Larijani. A hard-line cleric appointed by Iran's supreme leader, Ayatollah Ali Khamenei, Larijani is a highly influential member of Iran's most powerful political family. His older brother, Ali Larijani, is the speaker of Iran's parliament.
Iran's judicial system is notoriously repressive, and the country remains one of the world's leading executioners. According to the European Union, which placed its own sanctions on the judiciary chief in 2012, Sadegh Larijani has "personally signed off on numerous death penalty sentences."
"Naming and shaming Sadegh Larijani is one small way the U.S. can bring its human rights policy and coercive economic strategy against Iran into greater alignment," said Behnam Ben Taleblu, Iran expert at the Foundation for Defense of Democracies in Washington.
Other sanctions target companies accused of conducting prohibited transactions with Iranian entities. Malaysia-based Green Wave Telecommunications was named for providing U.S. technology to Iranian companies.
The Treasury Department also listed several Chinese individuals and companies for breaking similar rules to provide materials to Iran that could be used in navigation and weapons systems. Two Iranian companies that build and maintain the nation's military helicopters also are on the list.
"The designations today politically go to the top of the regime and send a very strong message that the United States is not going to tolerate their continued abuses, continued violations of the rights of their citizens," said an administration official, speaking on the condition of anonymity under rules for briefing reporters.
Erin Cunningham and Bijan Sabbagh in Istanbul and Karoun Demirjian in Washington contributed to this report.