- Video report by ITV News political editor Robert Peston
Theresa May has said she believes a Brexit deal is "still achievable" while being grilled by the House of Commons about the precise timings of the Irish backstop.
The questions came after the Government confirmed Brexit talks had run into a "significant problem" over the issue of the Northern Ireland border.
In her opening statement to the Commons, Mrs May said progress had been made on Northern Ireland but two problems remain - the EU's demands over the Northern Ireland backstop and the need for a time limit.
Mrs May called for "cool, calm heads to prevail" after talks last weekend failed to bridge differences between the UK and EU over the future status of the border in Ireland.
She told MPs: "I continue to believe that a negotiated deal is the best outcome for the UK and for the European Union.
"I continue to believe that such a deal is achievable.
"And that is the spirit in which I will continue to work with our European partners".
She also warned of the danger that failure to reach an agreement over the border could result in the UK leaving the EU without a deal in March next year.
The backstop is essentially an insurance policy to avoid a hard border between Northern Ireland and the Republic of Ireland.
Talks at the weekend stalled over the EU's demand for a "backstop to the backstop" designed to ensure the border between Northern Ireland and the Republic remains open under any circumstances.
Mrs May has offered to keep the whole of the UK temporarily in a customs union with the EU until a broader trade deal is in place avoiding the need for customs and regulatory checks at the Irish border, with the expectation this will not be later than the end of 2021.
But EU negotiator Michel Barnier insisted a carve-out keeping Northern Ireland alone in the EU's customs area should remain available in case the UK-wide arrangement lapses before the trade deal is finalised.
Mrs May told MPs this was not acceptable as it risked undermining the integrity of the UK.
The Prime Minister was addressing the House of Commons just two days before she travels to Brussels for a summit at which it had initially been hoped to finalise the UK's withdrawal agreement as well as a political declaration on future trade and security relations.
In the Commons, former foreign secretary Boris Johnson pushed for an exact date for when a backstop could end.
While Mrs May did not assure him of a precise date she said the expectation is that the backstop would last until December 2021.
However, she also said one of the problems with the Brexit talks is reflecting the "temporary nature" of the backstop.
Updating MPs on why Brexit talks had stalled she said: "First, the EU says there is not time to work out the detail of this UK-wide solution in the next few weeks.
"So even with the progress we have made, the EU still requires a “backstop to the backstop” – effectively an insurance policy for the insurance policy.
"And they want this to be the Northern Ireland-only solution that they had previously proposed.
"We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom".
She insisted that the EU and UK are not "far apart" in the Brexit talks.
"We both agree that Article 50 cannot provide the legal basis for a permanent relationship," she said.
"And we both agree this backstop must be temporary. So we must now work together to give effect to that agreement".
Labour leader Jeremy Corbyn dismissed Mrs May's comments as "another 'nothing has changed' moment from this shambles of a Government".
The impasse threatens to throw into disarray carefully choreographed plans which would have seen leaders of the remaining 27 EU states give the green light on Wednesday to a special summit in November to finalise the terms of the UK's withdrawal from the bloc.
It remains unclear whether Mrs May will be given the opportunity to address fellow leaders before they go into a working dinner to discuss Brexit in her absence.