The Most Reverend Justin Welby told ITV's Peston on Sunday that he “really genuinely” can't comprehend why fundamentalists have provided such a strong base for Mr Trump.
“There's two things going through my mind: do I say what I think, or do I say what I should say? And I'm going to say what I think,” he said on the show, referring to the support Trump has garnered, especially from so-called Evangelical Christians.
“No, I don't understand it. I really genuinely do not understand where that is coming from.”
The Archhbishop did say he would be willing to attend a state dinner in Trump's honour if the president comes to Britain on an official visit.
He noted that he has met with worse people than the president of the United States.
“I spent years and years involved in conflict stuff around the world where I met people who had killed many, many people,” he said.
He said part of his job is to meet with people he disagrees with “and to testify with the love of Christ to them and to seek to draw them in a different way.”
Trump has accepted an invitation for a state visit to Britain, but no date has been set.
Although he said he'd meet Mr Trump, he added: “It'd be unlikely I'd do more than shake hands with him.”
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