The Most Rev Justin Welby said it was "central to our future" as a country that the divisions were healed.
The Archbishop, speaking in the House of Lords, called on the Government to establish a "reconciliation unit" which would work across Whitehall departments and with humanitarian organisations and faith groups to bring people together.
The leading Church of England cleric, speaking at the start of a debate on role of reconciliation in British foreign, defence and international development policy, said: "This has been a week of deep division, and reconciliation will be something that, although applied to foreign policy in this debate, must become central to our future in this country.
"I hold firm to the belief that we can create a society where mutual flourishing is possible, disagreeing well is central and respecting the difference is paramount."
He added: "Reconciliation is needed before, during and after conflict, preemptive reconciliation is essential.
"I think it was Bill Shankly who said 'I teach my lads to get their retaliation in first'; we need to learn to get our reconciliation in first.
"Reconciliation happens from the top of society down, from the bottom of society up and from the middle of society out. It must include women, youth and minorities. If any group is left out, peace is not sustainable."
"What is needed is a joined-up approach to reconciliation, straddling humanitarian, economic, social, ethic, cultural, political, spiritual and religious factors in which different departments of Government work together under the umbrella of a joint reconciliation unit."
His calls for reconciliation come after a bruising week for Theresa May, in which she survived a confidence vote in her leadership.
Following the vote, the Prime Minister ventured to Brussels to seek concessions from the EU over the Northern Ireland backstop in a bid to get her Brexit deal through a heavily divided Commons.
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