BBC News 09 May 2018
Calling it "decaying and rotten", he said the deal was "an embarrassment" to him "as a citizen".
Going against advice from European allies, he said he would reimpose economic sanctions that were waived when the deal was signed in 2015.
Iran's President Hassan Rouhani said: "The US has announced that it doesn't respect its commitments.
"I have ordered the Atomic Energy Organisation of Iran to be ready for action if needed, so that if necessary we can resume our enrichment on an industrial level without any limitations."
He said he would "wait a few weeks" to speak to allies and the other signatories to the nuclear deal first.
"If we achieve the deal's goals in cooperation with other members of the deal, it will remain in place," he said.
The so-called Joint Comprehensive Plan of Action (JCPOA) curbed Iran's nuclear activities in return for the lifting of sanctions that had been imposed by the UN, US and EU.
Mr Trump had previously complained that the deal only limited Iran's nuclear activities for a fixed period; had failed to stop the development of ballistic missiles; and had handed Iran a $100bn (£74bn) windfall that it used "as a slush fund for weapons, terror, and oppression" across the Middle East.
"It is clear to me that we cannot prevent an Iranian nuclear bomb under the decaying and rotten structure of this deal," Mr Trump said.
"The Iran deal is defective to its core."
Former President Barack Obama, who signed the deal on behalf of the US three years ago, called Mr Trump's announcement "misguided".
The US Treasury said economic sanctions would not be reimposed on Iran immediately, but would be subject to 90-day and 180-day wind-down periods.
In a statement on its website, it said sanctions would be reimposed on the industries mentioned in the 2015 deal, including Iran's oil sector, aircraft exports, precious metals trade, and Iranian government attempts to buy US dollar banknotes.
US National Security Advisor John Bolton is reported as saying that European companies doing business with Iran will have to finish within six months or face US sanctions.
The UK, France and Germany urged the US not to obstruct its implementation. They said they would work with the other signatories to the 2015 deal - Russia and China - which have stressed continuing support for the accord.
Other signatories to the deal have been left aghast. Russia said it was "deeply disappointed" by Mr Trump's decision.
The French Foreign Minister, Jean-Yves Le Drian, insisted the deal was "not dead" and said there would be a meeting between France, Britain, Germany and Iran on Monday.
Former President Barack Obama - who played a key role in the agreement said on Facebook that it was working and protected US interests.
"Walking away from the JCPOA turns our back on America's closest allies, and an agreement that our country's leading diplomats, scientists, and intelligence professionals negotiated," he said.
But the move has been welcomed by Iran's major regional rivals, Saudi Arabia and Israel.
Israeli Prime Minister Benjamin Netanyahu, a prominent critic of the accord, said he "fully supports" Mr Trump's withdrawal from a "disastrous" deal.
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