Most Rev Justin Welby urged the leader to remove the content from his official Twitter page and clarify his position on racism.
Writing on Facebook, he said: "I join the urgent call for President Donald Trump to remove his Britain First retweets and make clear his opposition to racism and hatred."
Mr Trump retweeted three posts published by the deputy leader of Britain First, Jayda Fransen, to his 43.6 million followers on Twitter.
The videos claim to show Muslims committing crimes, although none have yet been verified and at least one has been identified as fake.
Archbishop Justin added: "It is deeply disturbing that the President of the United States has chosen to amplify the voice of far-right extremists.
"Britain First seeks to divide communities and intimidate minorities, especially our Muslim friends and neighbours."
Mr Trump's actions have also been condemned by Labour leader Jeremy Corbyn, the Communities Secretary Sajid Javid and Brendan Cox, the widower of MP Jo Cox who was murdered by an extremist who shouted "Britain first".
Archbishop Justin went on to say: "God calls us as Christians to love our neighbour and seek the flourishing of all in our communities, societies and nations."
Jayda Fransen, 31, was convicted in November 2016 of religious aggravated harassment after verbally abusing at Muslim woman wearing a hijab.