"From listening to those views it is clear that while there is broad support for key aspects of the deal, on one issue, the Northern Ireland backstop, there remains widespread and deep concern".
Her Downing Street office insisted that the vote will go ahead despite speculation that the government may be forced to delay it.
In a statement, opposition Labour Party leader Jeremy Corbyn said the vote's postponement was evidence that "we don't have a functioning government". EU leaders have ruled out any change to the divorce deal but some EU officials have mentioned the possibility of changes to the accompanying political declaration on future trade ties between Britain and the EU after Brexit.
The pound fell 1.6 percent against the dollar to as low as $1.2507 (GBP=D3), most of the loss coming after May confirmed she was delaying the vote.
"In our - admittedly low confidence - base case, stress in financial markets and pressure from businesses should lead to a last-minute approval of the deal in parliament", said Silvia Dall'Angelo, senior economist at Hermes Investment Management.
"Deferring the vote is only of any use if the Government is prepared to go to Brussels and insist on necessary changes to the Withdrawal Agreement", the North Belfast MP said.
Ahead of her statement, Mrs May spoke by phone to Arlene Foster, leader of the Democratic Unionist Party, whose MPs prop up the minority Conservative administration but were threatening to vote against her deal.
"As President Juncker said, this deal is the best and only deal possible", she said.
Britain's Prime Minister Theresa May tours the Royal Welsh Winter Fair at the Royal Welsh Showground in Builth Wells, Wales, Britain.
"We have a responsibility to discharge [it]", she said. He says "the government has lost control of events and is in complete disarray".
May now faces the threat of a no-confidence motion, which would end the rule of her government, if successful. "This shambles can't go on - so how about it?" Her spokeswoman briefed reporters on Monday that there was no plan to pull the vote. The measure would keep Britain under European Union customs rules, and is supposed to last until it is superseded by permanent new trade arrangements. But critics say it could leave Britain tied to the European Union indefinitely, unable to strike new trade deals around the world.
The deal had been scheduled to be debated in the House of Commons on Monday with particular attention being paid to the potential impact of the deal on relations within the UK.
"The deal is the deal", Irish Foreign Minister Simon Coveney said Monday. "It's a fair deal for both sides". "Just keep in mind that we will never let the Irish down". The majority of British voters, who decided in a 2016 referendum to leave the European Union, would be "shocked and very angry" if Brexit were halted.
The Luxembourg-based court ruled on Monday (10 December) that the United Kingdom was "free to revoke unilaterally that notification" after a "democratic process in accordance with national constitutional requirements".
Brexit Secretary Stephen Barclay will then make a statement to MPs on the Article 50 process.
Responding to Mrs May's statement, Mr Corbyn said there was no point in her bringing back the same deal to the House further down the line.
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