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 UK has a clear position on the Iran nuclear deal: we regard it as a crucial agreement that makes the world a safer place by neutralizing the threat of a nuclear-armed Iran", the British Foreign Office said.
America's allies see the accord as the best way of thwarting Iran's quest for nuclear arms and a victory for multilateral diplomacy.
Trump's declaration puts great pressure on Britain, France and Germany, the European signatories to nuclear pact with Iran.
United States officials expect the White House to issue a statement later Friday to confirm that Trump has grudgingly signed the sanction waivers once again before they start to expire this weekend - though he is also expected to impose new sanctions on Tehran over non-nuclear issues.
Russian Federation on Saturday said Washington would be making a grave mistake by pulling out of the Iran nuclear deal, adding that Moscow would work hard to keep the landmark agreement alive.
The 2015 deal, known as the Joint Comprehensive Plan of Action, was signed by the U.S. under the previous administration of president Barack Obama as well as Iran, China, Russia, Britain, France and Germany. All sides agreed that it would cover only Iran's apparent efforts to develop nuclear weapons, which was in violation of United Nations resolutions, and not other issues.
While there may be some relief that Trump has yet to torpedo the hard-won accord, there were clear signs of frustration from European capitals in the runup to the decision.
Trump also wants Iran's ballistic missile programme to be addressed.
The president's proposals to "fix the deal's disastrous flaws" include Iran's agreement to open all sites immediately to global inspectors and an assurance from Tehran that it will never develop a nuclear weapon.
The cyber unit of the Islamic Revolutionary Guard Corps, which the Trump administration maintains has stifled social media networks that demonstrators can use to communicate, was also blacklisted.
Trump extended the waivers of key sanctions that were lifted as part of the Obama-era agreement Friday, but he said it was the last time.
Trump is required to renew the existing deal every 120 days under U.S. law.
Republican Senator Bob Corker said "significant progress" had been made on bipartisan congressional legislation to address "flaws in the agreement without violating USA commitments".
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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