Speaking during ITV's Peston on Sunday, Most Rev Justin Welby also rebuked the US President over his "completely unacceptable" views about women.
Asked his opinion about Mr Trump's following among "fundamentalist" believers, the Anglican leader answered: "I really, genuinely, do not understand where that is coming from."
An exit poll published after last year's US Presidential election by the Pew Research Center suggested that 81-per-cent of people identifying as 'white, born-again, evangelical Christians' chose Mr Trump over Hillary Clinton.
Quizzed over whether he would attend any UK state dinner held in Donald Trump's honour, Archbishop Welby said he would not shun the event, adding "the odds are, it would be unlikely I'd do more than shake hands with him."
The US leader is set to visit Britain early next year however the initial state visit he was promised is being scaled back, amid speculation such a formal welcome could trigger mass protests.
Archbishop Justin said: "Part of the job [as Archbishop] is to meet people you disagree with and to testify of the love of Christ to them, and to seek to draw them into a different way."
Controversy surrounding alleged comments made by the US President prompted the Daily Telegraph newspaper to publish its 'Donald Trump sexism tracker' in July.