South Korea’s President has reportedly suggested Mr Trump should win the honour for his efforts to unify Korea.
When asked if he agreed with such a view, the Foreign Secretary said: “If he can fix North Korea, and he can fix the Iran nuclear deal, then I don’t see why he’s any less of a candidate for the Nobel Peace Prize than Barack Obama, who got it before he even did anything.”
Mr Obama was controversially awarded the prize in 2009, less than a year after entering office.
Mr Johnson was speaking during a trip to Washington DC, where he is trying to convince President Trump to renew the 2015 agreement with Tehran.
Mr Johnson warned Mr Trump that Iran will “go for a bomb” if the deal is scrapped.
The Foreign Secretary said that deal is “working” at its core, and the US and its allies should work to “fix the rest”.
Mr Trump is due to decide on whether the agreement should be renewed on 12 May.
He has previously described the deal as “insane” and issued an ultimatum in January to “either fix the deal’s disastrous flaws, or the United States will withdraw”.
The agreement eased sanctions on Tehran in exchange for commitments to abandon its nuclear weapons programme.
Mr Johnson said: “The president set the world a legitimate challenge in January, which is to try and address a lot of the bad stuff that Iran is doing in the region.
“To try to stop Iran getting missiles, intercontinental ballistic missiles.
“Stop them interfering in neighbouring countries, and also to fix the core problem of the deal, which is that it expires in 2025, and then there’s no way of stopping that it expires in 2025, and then there’s no way of stopping the Iranians going very rapidly to get a nuclear weapon.”
Mr Johnson added that the US President has “a point” when it comes to what will happen when the agreement expires, but added there is currently “no plan B” if the deal is scrapped.
Touching on the agreement’s uncertain future, he continued: “There could well be a collapse of the deal, and what happens then? The Iranians just go for a bomb. And how do we stop them? What’s our plan B?
Mr Johnson continued: “We have a deal at the moment that is working. The IAEA has done 400 inspections. We’ve been able to reduce Iran’s centrifuges by two-thirds, their enriched uranium by 95%.
“These things are working, so keep the core of it, fix the rest.”
The Foreign Secretary was later asked if he felt that Mr Trump might be distracted by the Stormy Daniels affair.
The President’s former lawyer is said to have paid $130,000 to an adult actress not to share claims she had an affair with Mr Trump in 2006.
Mr Trump’s new lawyer Rudy Giuliani has said it is possible the President’s former attorney paid other women.
Turning to Brexit, Mr Johnson was asked if he would resign if he doesn’t “get the deal on the customs union” that he wants in the negotiations.
He replied: “The Prime Minister has made it very clear as she said in her Mansion House speech – we’re coming out of the customs union, we’re coming out of the single market, we’re taking back control of our laws.”
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Mr Johnson also appeared on Mr Trump’s favourite show Fox & Friends, where he urged the President not to “throw the baby out with the bathwater” over the Iran deal.
He added that “plan B does not seem, to me, to be particularly well developed at this stage”.