Speaking in the House of Lords, Justin Welby also said it would a moral failure should the UK leave the European Union without a deal.
The Anglican leader was taking part in a debate in the upper chamber as MPs continued talks in the Commons next door ahead of a vote on the Prime Minister's plan next Tuesday.
Welby said: "There has to be an agreement in which all accept the need to deliver the will of the people, which was expressed in the referendum. While also recognising that when it was expressed in such a close result there is a duty to build in compromise, an inevitability, albeit unwelcome to some.
"If not there will by default be a no-deal Brexit. That outcome would be not only be a political and practical failure but a moral one, equally as serious as ignoring the result of the referendum entirely.
"My Lords, a second referendum is not my preference, but if Parliament fails in the task entrusted to it, then regrettably it may be required. This is about more than Brexit, and Parliament must not show itself unfit for the job."
The archbishop also encouraged MPs to work selflessly to ensure the UK thrives going forward.
He said: "As we embrace a challenge that I believe is hope-filled and exciting, of reimagining our country and its structures over the next few years and months, I hope politicians will take it upon themselves to make these crucial decisions not only with the grand vision, but also with 'the small picture' - the effect on local people, communities and businesses - in mind as well."
His comments comes just a week after his New Year's message in which he called on the UK to overcome division in 2019.