The Prime Minister was due to address leaders of the 27 remaining EU states before they discuss Brexit in her absence at the European Council on Wednesday evening.
The UK is scheduled to leave the European Union in five and a half months but so far there has been no agreement on how that should be done, and how 45 years of common legislation in everything from trade to pesticides should be untangled.
Former Ukip leader Nigel Farage said that it would delay full withdrawal nearly until the general election scheduled for May 2022 and "may mean we never leave at all".
But following a short presentation from May, EU leaders said she had brought nothing new to Brussels.
"There are some hard issues we are still working through".
The DUP's support is crucial for the continuation of May's government after her party lost the majority in parliament following a snap election a year ago and the Tories and the DUP signed a confidence-and-supply deal which effectively means the DUP helps keep the Conservatives in power. "The last stage will need courage, trust and leadership on both sides", she said.
Despite all this, Mrs May says she is still convinced she will get a deal on Britain's withdrawal from the EU.
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"This prolongation of the transition period probably will happen". Tajani said May told him she would consider it but gave no indication of whether she favoured such an extension. "It's a matter concerning Britain's political ability to find a presentable agreement".
But she later accepted a 21-month transition offered by the European Union, ending on the last day of December 2020.
Danielle Haralambous, U.K. analyst at the Economist Intelligence Unit, told CNBC via email: "With the current phase of negotiations in deadlock over the Irish border issue, an extension of the transition period could in theory provide more time to negotiate a trade arrangement that permanently solves it".
"If the United Kingdom decided that an extension of the transition period would be helpful to reach a deal, I am sure that the leaders would be ready to consider it positively", Tusk said.
The possibility of an extension made front-page news in Britain on Thursday and some eurosceptic MPs warned they could not accept such a plan.
But May was under attack from across Britain's political spectrum after saying she's considering a European Union proposal that would keep the United Kingdom bound to the bloc's rules for more than two years after it leaves on March 29.
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The thorny issue of the border between Ireland and the British province of Northern Ireland could sink the negotiations on Britain's exit from the European Union, the EU's chief Brexit negotiator Michel Barnier said on Friday (19 October).
However, Brexiteers have reacted with anger at suggestions the UK's stay within the EU's structures could be lengthened beyond what had previously been agreed as a 21-month period.
Nonetheless, the European institutions said Monday that their preparations for a no-deal scenario were being intensified.
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Mr Macron, who held separate talks with Mrs May ahead of the three-hour dinner, said it was time to "accelerate" talks.
It might be hard for May to convince her Cabinet and parliament of an extension of the transition period, however.
At the close of the EU Council summit, Theresa May said Brexit talks "were always going to be tough" and insisted a deal could still be reached.
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