Before the summit, Germany's Chancellor Angela Merkel issued a stern warning that Europe must be prepared for a no-deal Brexit, while France has also stepped up its planning for the potentially catastrophic scenario.
Neither side has shown much sign of flexibility, but diplomats say European Union negotiator Michel Barnier is willing to add a year to the 21-month post Brexit transition period - taking it to the end of 2021.
"We should not call a summit just to talk", the Taoiseach said.
He added that Brexit must be "orderly" and that more time was needed to work issues out "calmly and patiently". "We need time, we need much more time..."
The ongoing Brexit talks will explore extending the transition period, during which nothing will change after Brexit in March 2019.
"Both sides mentioned the idea of an extension of the transition period as one possibility which is on the table and would have to be looked into", he added.
Number 10 did say progress had been made on the vital issues of the future trade framework, and the notion of a whole United Kingdom backstop for both customs and some single market regulations.
Extending the transition period could mean that if a future partnership is not ready, a backstop, which so far has been unpalatable to the British side, would not have to be triggered.
The Financial Times reported that EU Brexit negotiator Michel Barnier is open to a possible one-year extension to the Brexit transition, should Mrs May accept a "two-tier" backstop.
She is hemmed in by pro-Brexit members of her Conservative Party, who oppose any more compromises with the bloc, and by her parliamentary allies in Northern Ireland's Democratic Unionist Party, who insist a solution to the border issue can't include customs checks between Northern Ireland and the rest of the UK. "That would backfire spectacularly".
The day before the summit European Council chief Donald Tusk had urged May to come up with concrete proposals.
The lack of progress means a special European Union summit on Brexit that had been penciled in for next month to finalize a deal has been scrapped, though European Union leaders said they would assess the situation in the coming weeks.
"I'm convinced that if we as a government stand together and stand firm, we can achieve this", she said, according to her spokesman. "Where May certainly has to a certain extent a positive assessment of where we are, focused on the considerable progress that has been made on a number of issues and emphasises that a deal is in reach; and where I think the collective feeling among the EU27, I would say, is somewhat more sceptical and notes the lack of progress or at least the lack of agreement at this stage".
"Today there will be no breakthrough", said Lithuanian President Dalia Grybauskaite.
"Today we do not know what they want". They do not know themselves what they want.
However, an extension does not in and of itself solve May's problem, which is that she has yet to fully decide, let alone agree, what sort of relationship she wants to secure during that additional transition period. "There is still time for the drama to play". Westminster rises on December 20 for Christmas.
Visiting North East Derbyshire, Ashfield and Bolsover, the Labour leader will express understanding of the reasons for which people voted to leave the EU.
Last night, it was suggested amendments would only be taken if the main Brexit motion was passed.
Mr Raab noted: "Anything other than a straightforward approval of the deal will bring with it huge uncertainty for business, consumers and citizens".
But he said she was "not against" the idea of extending the transition, a position confirmed by the European Union official.
Ailleurs en Europe, on observe une croissance en Pologne et en Roumanie, mais un recul en Espagne (-2,7%) et en Italie (-4,4%). Pour rappel, c'est Gérard Lavinay , bien connu chez nous pour avoir dirigé les opérations belges, qui fut nommé.
That's what it's called when it's tied to consumption of contaminated beef, but in this case, doctors suspect a different culprit. A man has died after he developed a rare and fatal infectious disease from eating squirrel brains, likened to mad cow disease .
Il poursuit: "La clé était d'attaquer et quand j'ai vu Nibali attaquer dans le Sormano, j'ai dit, 'Bingo, c'est le bon coup'". ". Pour parachever son triomphe, Pinot a su parfaitement maîtriser la course et produire son effort au bon moment.
And now Alia is back with her beau, in New York City to support him as his ailing father undergoes treatment at a hospital there. Last month, Rishi Kapoor had put a tweet, announcing that he is visiting the United States for a medical treatment.
En effet, de forts vents ont causé certains ennuis, au cours de la nuit de lundi à mardi, dont des pannes d'électricité. Ce sont principalement des arbres et des branches brisés par le vents qui cause les interruptions de courant.
Some police were in uniform while other officials were in suits carrying printers and files, an AFP correspondent said. The Saudi stock market had tumbled 7.2 percent over the previous two trading days but rebounded 2 percent on Monday.
Kerber se sépare de son entraîneur — WTA
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Neymar Wants a Return to Spain and the La Liga
Luis Suarez and Ivan Rakitic were also some of Neymar's close acquaintances and he still considers Barcelona as "his club". Mbappe joined PSG from Monaco weeks after Neymar's arrival.