JD Vance made the remarks at a conference for UK Conservatives last week.
JD Vance, who has been named former US President Donald Trump's running mate, stirred a controversy after he said that that UK under Labour might be the first "truly Islamist" country with nuclear weapons.
Vance said he had been discussing with a friend which country would be the first "truly Islamist country that will get a nuclear weapon".
"Maybe it's Iran, maybe Pakistan kind of counts, and then we sort of decided maybe it's actually the UK since Labour just took over," he said last week at a conference for UK Conservatives last week.
Britain's Deputy Prime Minister Angela Rayner, meanwhile, played down Vance's comments, saying he had a history of making "fruity" remarks.
Britain would work with whoever won November's US presidential election, Angela Rayner said, adding that "I don't recognise that characterisation".
"We're interested in governing on behalf of Britain, and also working with our international allies," she said.
In one of his first interviews after being named the Vice Presidential pick, Vance also branded China the biggest threat to America, underscoring the likely hawkish stance of their administration toward Beijing if elected.
The Ohio Senator made the remarks in an interview with Fox News' Sean Hannity on Monday. When asked about the war in Ukraine, Vance said Trump would negotiate with Moscow and Kyiv to "bring this thing to a rapid close so America can focus on the real issue, which is China."
"That's the biggest threat to our country and we are completely distracted from it," he said
Vance, 39, was tapped by Trump days after a failed assassination attempt on the former president upended what had already been a chaotic presidential contest.