Foreign Secretary Boris Johnson said Britain had no intention of walking away from the deal, known as the JCPOA. He also said Britain would do its utmost to protect UK commercial interests in Iran.
"Now that the Trump administration has left the JCPOA, the responsibility falls on them to describe how they in Washington will build a new negotiated solution to our shared concerns," he told parliament.
"President Trump said himself last night that he is committed to finding a new solution and we should hold him to his word."
Johnson said he had no problem with Trump's goal for a lasting solution to Iran's nuclear threat and other Iranian policies seen as malign by London and Washington, but added: "The question is: how does the U.S. propose to achieve it?"
Asked about the potential impact of new U.S. economic sanctions against Iran on British firms seeking to do business in the country, Johnson did not go into specifics but indicated the government would be supportive of companies.
"We will do our utmost to protect UK commercial interests," he said.
Asked what suggestions the British government would be making to the U.S. administration about the way ahead in dealing with Iran, Johnson talked about the idea of a follow-on agreement that would preserve the central pillars of the JCPOA while addressing other issues beyond the nuclear programme.
Throughout his statement, Johnson repeatedly said the JCPOA had delivered on the core goal of preventing Iran from moving towards acquiring a nuclear bomb. He also said the central bargain of the deal, better economic prospects for Iran in return for de-nuclearisation, remained valid.
"We did our utmost to prevent this outcome. From the moment that President Trump's administration took office, we made the case for keeping the JCPOA at every level," he said.
"The U.S. decision makes no difference to the British assessment that the constraints imposed on Iran's nuclear ambitions by the JCPOA remain vital for our national security and the stability of the Middle East.
"For as long as Iran abides by the agreement ... then Britain will remain a party to the JCPOA," he added. "Britain has no intention of walking away."
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