The Foreign Secretary will point to the success of the Iran deal while calling for "toughness but engagement" with Pyongyang following increasingly warlike rhetoric between the US President and Kim Jong-un.
In a speech in London, Mr Johnson will say the President was right to keep military action on the table in the face North Korea's increasing nuclear capabilities but he will also praise US Secretary of State Rex Tillerson for opening the door to talks.
It comes after Mr Trump described the North Korean leader as “Rocket Man on a suicide mission” and threatened to “totally destroy” the pariah state in his first speech to the United Nations General Assembly.
Mr Trump also drew international concern when he decertified the 2015 pact with Iran and last week repeated threats to pull out of the landmark deal.
The Foreign Secretary will urge Mr Trump to invoke the spirit of the 1970 nuclear non-proliferation treaty (NPT), which avoided a "Gadarene Rush to destruction" by turning the world into a "great arena of Mexican stand-offs".
Speaking at the Chatham House annual conference, he will praise the "extraordinary" achievement of the treaty which has contributed to the "unprecedented epoch of peace and prosperity that we have all been living through".
Mr Johnson will add: "It has helped avoid what might otherwise have been a Gadarene Rush to destruction, in which the world was turned into a great arena of Mexican stand-offs, a nuclear version of the final scene of Reservoir Dogs.
"That far-sightedness is now needed more than ever, not only to keep the NPT, but also one of its most valuable complementary accords, the nuclear deal with Iran."
Mr Johnson will praise Mr Tillerson for reinforcing South Korea's promises not to seek regime change in the North or seek to deploy forces over the border or reunify the pensinsula, saying they opened up a path to talks and de-escalation.
But stressing the need to keep military options on the table, he will say: "That is the model - of toughness but engagement, each reinforcing the other - that we should have at the front of our mind as we try to resolve the tensions in the Korean peninsula."
He will urge the North Korean regime to change course and show that it is once again capable of the "diplomatic imagination" that produced the nuclear non-proliferation treaty and the Iran deal.
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