Mr Burt, a Christian, supported an amendment on Monday evening which allows Parliament to take control of the House of Commons agenda tomorrow. MPs will vote on several options for how the UK might leave the EU.
The 63-year-old minister for North Africa and the Middle East said: "Despite the best and determined efforts of the Prime Minister, her agreement with the EU continues to be rejected by Parliament.
"We are running out of time for an alternative, and the risk of leaving without a deal, and continuing serious and disruptive uncertainty is affecting the UK profoundly."
Mr Burt, who first sat in Parliament in 1983, had been the Government's Middle East minister since June 2017.
Sad to see dear friend @AlistairBurtUK leave @ForeignOffice once again. Will miss his faithful and informed insight and contribution into #MENA region.
— Archbishop Angaelos ن (@BishopAngaelos) March 26, 2019
Another sad outcome of the instability we currently live. Praying peace and stability for our nation.https://t.co/1Id8VvtsyT
He was among MPs who attended a speech at the Palace of Westminster in December 2017 by an Iraqi priest who bought the remains of a Bible burned by Islamic State with him.
The Coptic Archbishop of London, Archbishop Angaelos said: "I am sad to see dear friend Alistair Burt leave Foreign Office once again.
Statement on my resignation from Government last night: https://t.co/5ZXE8bRcOb
— Alistair Burt (@AlistairBurtUK) March 26, 2019
"Will miss his faithful and informed insight and contribution into Middle East and North Africa region. Another sad outcome of the instability we currently live. Praying peace and stability for our nation."
In a statement published online, Mr Burt added: "Parliament should seek urgently to resolve the situation by considering alternatives freely, without the instruction of party whips, and Government should adopt any feasible outcome as its own in order to progress matters.
Following my decision last night, I wrote to the Prime Minister this morning confirming my resignation. pic.twitter.com/59yDDl594n
— Alistair Burt (@AlistairBurtUK) March 26, 2019
"I did not believe the Government was prepared to do that, so had to vote to ensure this happens.
"I remain a supporter of the Conservative Government, and the Prime Minister. But we have to come to a conclusion for the country's sake."
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