Britain, France and Germany "stand committed" to the Iran nuclear deal and are "concerned by the possible implications" of Donald Trump's refusal to back it, Theresa May, Angela Merkel and Emmanuel Macron said in a joint statement.
The US president accused Tehran of violating the spirit of the landmark 2015 agreement and is referring it to Congress.
Mrs May, the German Chancellor and French president said preserving the pact was "in our shared national security interest" and called for Washington to "consider the implications" of taking action that undermines it.
Mr Trump stopped short of ripping up the deal but said without measures to toughen it up "the agreement will be terminated".
The statement from the UK, France and Germany said the International Atomic Energy Agency (IAEA) had "repeatedly confirmed" Iran's compliance to the terms it signed up to.
It said: "We, the leaders of France, Germany and the United Kingdom take note of President Trump's decision not to recertify Iran's compliance with the Joint Comprehensive Plan of Action (JCPoA) to Congress and are concerned by the possible implications.
"We stand committed to the JCPoA and its full implementation by all sides. Preserving the JCPoA is in our shared national security interest. The nuclear deal was the culmination of 13 years of diplomacy and was a major step towards ensuring that Iran's nuclear programme is not diverted for military purposes."
It added: "We encourage the US administration and Congress to consider the implications to the security of the US and its allies before taking any steps that might undermine the JCPoA, such as re-imposing sanctions on Iran lifted under the agreement.
"At the same time as we work to preserve the JCPoA, we share concerns about Iran's ballistic missile programme and regional activities that also affect our European security interests.
"We stand ready to take further appropriate measures to address these issues in close cooperation with the US and all relevant partners. We look to Iran to engage in constructive dialogue to stop destabilising actions and work towards negotiated solutions."
Foreign ministers have been asked to "consider with the US how to take these issues forward", it said.
Shadow foreign secretary Emily Thornberry accused Mr Trump of an "act of wanton vandalism" and said it was "high time" the Government stopped kow-towing to the US president and challenged him on his actions.
She said: "It is an act of wanton vandalism for Donald Trump to jeopardise the future of that deal today, and to move the goalposts by linking it to important but utterly extraneous issues around Iran's wider activities in the region.
"It is also totally disingenuous to suggest that the deal just needs to be fixed, when the only evidence that it is any way broken is inside Donald Trump's head.
"Yet sadly, this kind of reckless and thoughtless behaviour is what we have come to expect from this President.
"From the Paris climate change deal to US membership of Unesco, he has demonstrated a flagrant disregard for the institutions and agreements that bind the international community together in the shared pursuit of a better future.
"That is not what we expect from the President of the United States, and it is high time for the British government to tell him so.
"Because yet again, this shows that the strategy of kow-towing and hand-holding operated by the Prime Minister and Foreign Secretary has utterly failed, and they have once more allowed our so-called closest ally to treat them like fools.
"When he fooled Theresa May and Boris Johnson on climate change, we can say shame on him, but now the same pair have been fooled on Iran as well, we can only say shame on them."
Tory former chancellor Lord Lamont, UK trade envoy to Iran and chairman of the British Iranian Chamber of Commerce, said the president had "undermined trust in the United States".
"Why should anyone make an agreement with the US again?" he said.
"No one other than President Trump believes Iran has broken the agreement. Who should we believe, the US president or the IAEA?
"This decision undermines the position of the pragmatic president of Iran, President Rouhani, who wants to open his country up to the rest of the world.
"The people who will be most pleased by this announcement will be hardliners in Iran. This is their moment when they say 'we told you so, never trust America'."
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