The call came in an op-ed piece in The New York Times that was signed by Foreign Secretary Boris Johnson, ahead of a meeting with officials from the US administration in Washington on Monday.
Trump has threatened to withdraw from the agreement when it comes up for renewal on May 12, demanding his country's European allies "fix the terrible flaws" in it or he will re-impose sanctions on Iran that were eased under the historic accord.
The nuclear deal was struck in 2015 among Iran and Britain, China, France, Germany, Russia and the United States, then led by Barack Obama.
Under the pact, sanctions were eased in return for a commitment from Iran not to pursue a nuclear bomb, but Iran says it is not reaping the rewards despite complying with the deal.
"At this delicate juncture, it would be a mistake to walk away from the nuclear agreement and remove the restraints that it places on Iran," Johnson wrote in the Times piece.
He argued that inspectors from the International Atomic Energy Agency have been granted extra powers to monitor Iran’s nuclear facilities, "increasing the likelihood that they would spot any attempt to build a weapon".
"Now that these handcuffs are in place, I see no possible advantage in casting them aside. Only Iran would gain from abandoning the restrictions on its nuclear program," Johnson wrote.
He added: "I believe that keeping the deal's constraints on Iran's nuclear program will also help counter Tehran's aggressive regional behavior. I am sure of one thing: every available alternative is worse. The wisest course would be to improve the handcuffs rather than break them."
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