Trump has said that unless European allies rectify "flaws" in Tehran's deal with world powers by May 12 he will refuse to extend US sanctions relief for Iran.
Trump has threatened to withdraw from the deal, which provided Iran with relief from economic sanctions in exchange for limiting its uranium enrichment capacity, unless European signatories to the accord fix what he has called its shortcomings.
"If you do that you have to answer the question what next?" German Chancellor Angela Merkel acknowledged that possibility in a January conversation with Israeli Prime Minister Benjamin Netanyahu, according to news site Axios, that quoted Merkel as saying: "It will put us, the Brits and the French on the same side with Russia, China and Iran when the USA and Israel will be on the other side".
In a separate interview during the visit, Mr Johnson raised the prospect of Mr Trump winning the Nobel Peace Prize. Is that a realistic possibility?' "I can't believe the rest of the world has to put up with the stuff right now, like we don't have other problems on our mind at the moment?"
The decision to award Mr Obama the prize in 2009 just a short time after he entered the White House proved controversial.
The UK's ambassador to the United States Sir Kim Darroch said the Iran agreement was "a good deal" but efforts were ongoing to "find some language, produce some action that meets the president's concerns".
Under the agreement with the United States, France, Germany, Britain, Russia and China, Iran strictly limited uranium enrichment capacity to try to show that it was not trying to develop atomic bombs.
Under its terms, Iran is committed to a peaceful nuclear energy programme.
"It has weaknesses, certainly, but I am convinced they can be remedied", Johnson wrote in an opinion piece for the New York Times.