Dr John Sentamu said rejecting the proposed deal "without the prospect of an alternative" would be to "betray" the trust people have placed in politicians.
In a letter published by the Yorkshire Post, he said: "To act in ways that bring about the collapse of a government's position without the prospect of an alternative would be to betray the trust we place in our representatives."
Acknowledging how he voted to remain in the EU during the 2016 referendum, Dr John warned that holding a second referendum on Brexit would undermine public trust and established decision-making procedures.
He continued: "Our first concern must be maintaining respect for democratic law-making institutions, which are under heavier pressure today than for more than a century.
In his own words: @JohnSentamu on why he backs the #Brexit deal as he appeals to MPs to work together to reconcile the country's future https://t.co/OJoD8c1VJP@JayMitchinson@RobParsonsYP@IanDayPix@singharj@Reportereditor@DioceseofYork#York@BBCr4today#TheresaMay@ConHome— OpinionYP (@OpinionYP) December 3, 2018
"Permanent loss of confidence in governmental institutions always results in civil unrest and violence."
The Anglican leader also wrote about the need to preserve "positive relations" with "those who have been our neighbours immemorially, and will be our neighbours so long as life continues on this continent."
Speaking ahead of a crunch vote by MPs on the draft Brexit withdrawal agreement on Tuesday 11th December, Dr John said MPs had a "duty" to "bring order out of... chaos".
Last month,t he Archbishop of Canterbury said churches must "strive for reconciliation" in the face of Britain's withdrawal from the European Union, as some politicians try to "drive a wedge between people".
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