Prime Minister Theresa May has insisted that a Brexit deal is still "achievable" despite deadlock in negotiations just days ahead of a crunch European Council summit.
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.
And she warned of the danger that failure to reach agreement over the border could result in the UK leaving the EU without a deal in March next year.
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.
Following the failure to achieve a breakthrough when Brexit Secretary Dominic Raab met EU chief negotiator Michel Barnier on Sunday, the European Commission confirmed that no further negotiations will be held ahead of Wednesday's summit.
German Chancellor Angela Merkel said the prospect of agreement "looks a bit more difficult again", adding: "If it doesn't work out this week, we must continue negotiating, that is clear – but time is pressing."
Berlin wants the UK's withdrawal next March to be orderly "but not at any price", Mrs Merkel told a conference of German exporters.
And Irish Taoiseach Leo Varadkar suggested a deal may be delayed as late as December.
Mr Varadkar said Dublin was making preparations for a "potentially catastrophic" no-deal withdrawal, but did not believe that this was the most likely outcome.
But Sammy Wilson, Brexit spokesman for the DUP, which props up Mrs May's minority administration in the Commons, said that a no-deal outcome was now "probably inevitable" due to the "intransigence" of EU negotiators.
Talks at the weekend foundered over the EU's demand for a "backstop to the backstop" designed to ensure that 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 that this will not be later than the end of 2021.
But Mr Barnier insisted that 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 that this was not acceptable as it risked undermining the integrity of the UK.
The PM warned that the Irish issue must not be allowed to "derail" progress towards a deal which she said was in the interests of both the UK and EU.
She told MPs she would take steps to ensure that "we cannot be kept in this backstop arrangement indefinitely".
And she warned: "We are entering the final stages of these negotiations.
"This is the time for cool, calm heads to prevail.
"And it is the time for a clear-eyed focus on the few remaining but critical issues that are still to be agreed."
Mrs May voiced her "frustration" that the Irish border issue was holding up agreement on Brexit.
But she said: "We cannot let this disagreement derail the prospects of a good deal and leave us with the no-deal outcome that no-one wants.
"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."
Labour leader Jeremy Corbyn dismissed Mrs May's comments as "another 'nothing has changed' moment from this shambles of a Government".
Mrs May's call for calm came after former foreign secretary Boris Johnson said talks were "entering the moment of crisis" and urged the PM to reject the EU's offer and scrap the backstop.
"The EU is treating us with naked contempt ... (offering) a choice between the break-up of this country or the subjugation of this country, between separation or submission," Mr Johnson told the Daily Telegraph.
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.
Reports from Brussels suggest that the EU27 are now considering using the mooted November summit to discuss preparations for a no-deal Brexit.
With Mrs May under siege from Tory Eurosceptics and her DUP parliamentary allies, her room for manoeuvre is severely restricted.
Although the absence of a deal has damped down expectations of ministerial resignations, Eurosceptic Cabinet members are reported to be planning to meet over pizza on Monday evening to co-ordinate their stance.
Asked whether Mrs May regarded the so-called "pizza summit" as helpful, the PM's spokesman said: "Cabinet ministers are free to eat whatever they choose. Cabinet colleagues have discussions with each other all the time."
The febrile atmosphere in the Tory ranks has seen former Brexit secretary David Davis emerge as a potential successor to Mrs May, with allies saying he had been contacted by several MPs urging him to run for the leadership.
Tory MP Nadine Dorries said: "Getting May out and him becoming an interim leader may be the only way to deliver Brexit."