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."