It comes after the Archbishop told those who voted to stay in the EU to "stop whingeing" and accept the verdict of the Brexit vote at a Christian festival last week.
Welby shared on social media his regret over hurting people's feelings with his "careless" and "insensitive" remarks saying: "I am aware of the upset after I talked about the need to "stop whingeing" about the Brexit referendum result.
"I expressed myself carelessly and insensitively in the moment. I apologise for that and the hurt that people have felt."
He went on to say that Christians have a responsibility to be "salt and light" and to "admit when they go wrong."
In his Facebook post the Archbishop insists the intention of his comments was to discourage hateful language and promote unity and reconciliation at a time of great division across the country.
He went on to say that although he has concerns over the political climate and the implications a no-deal Brexit could have on the poor, he recognises that all Christians are united by their faith in Christ, regardless of their politic views.
"I remain concerned about the risks of No Deal Brexit for the people least able to bear them. These risks may or may not turn out to be reality, but we must be very sure that those who need protection are protected.
"What unites us is our faith in Jesus Christ. We recognise that through His undeserved love, there is hope and purpose and full life on offer to every person.
"There is no single Christian view of these matters. We all hold our different political beliefs and ideas within the love Christ calls us to have for each other, even our political opponents."
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