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 global sanctions.
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.
Iranian Foreign Minister Mohammad Javad Zarif on Saturday said the world direly needs a cultural dialogue for security of all in Asia. "This is a last chance".
These penalties largely cut Iran out of the worldwide financial system, until they were suspended by Obama under the nuclear deal.
French President Emmanuel Macron called Trump on Thursday and stressed France's determination to see "the strict application of the deal and the importance of all the signatories to respect it".
Also on Friday, the United States imposed separate sanctions against 14 Iranian individuals and entities it accuses of rights abuses, censorship and support for weapons proliferators. Unilaterally re-imposing the sanctions would put the United States in violation of an global agreement that was unanimously approved by the United Nations Security Council in 2015.
The other signatories to the deal - Britain, China, France, Germany and Russian Federation - and the European Union, which oversaw the talks, were watching carefully.
"In the absence of such an agreement, the United States will not again waive sanctions in order to stay in the Iran nuclear deal".
One of the criticisms levelled at the nuclear deal is that it does nothing to address Iran's continuing ballistic missile program and involvement in conflicts such as Yemen and Syria.
European allies had strongly urged the White House to stick with the nuclear deal, saying a decision to abandon it would strain the transatlantic partnership.
But Trump, who must meet regular deadlines to endorse the deal every 90 days and approve sanctions waivers every 120 and 180 days, has railed against the agreement.
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 will never develop a nuclear weapon.
Trump is required to renew the existing deal every 120 days under United States law. It said the sanctions are against worldwide law and go against US commitments, saying they would bring a "strong reaction" from Iran.