By thus "decertifying" the arrangement, he opened a window for Congress to reimpose sanctions, but to date, it has not done so - leaving the issue of the waivers.
The U.N. nuclear watchdog agency has repeatedly found Iran is complying with those obligations.
He paired Friday's concession with other, targeted sanctions on Iran for human rights abuses and ballistic missile development.
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 July 2015, after a decade of strenuous negotiations, Iran and six major countries, namely, China, Russia, Britain, France, the US and Germany, struck a final agreement on Iran's controversial nuclear programme.
Meanwhile, on his official Twitter account, Iran's Foreign Minister Javad Zarif said Trump's decision undermined the multilateral agreement.
"This is a last chance", the United States president said in a statement on Friday. Mr. Trump is expected to decide by Friday whether to extend the sanctions relief or re-impose the restrictions his predecessor, President Barack Obama, suspended two years ago. "And if at any time I judge that such an agreement is not within reach, I will withdraw from the deal immediately", he warned.
Washington also announced sanctions against 14 entities and people, including the head of Iran's judiciary, Ayatollah Sadeq Larijani.
Trump is required to renew the existing deal every 120 days under USA law.
Britain, France and Germany had called on Trump on Thursday to uphold the pact.
United Nations inspectors have certified Iran's compliance with the deal nine times, most recently in November.
He did not set a deadline, but under USA law the president is required to waive sanctions every four months.
Russian Federation spoke out strongly Friday in favor of the accord, ahead of the announcement of Trump's decision, calling it "the result of a consensus among many parties", in the words of Kremlin spokesman Dmitry Peskov.
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.
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