"These issues are still pending, but in the talks I had this morning with Prime Minister Theresa May, we encouraged one another to reach an agreement on two out of the four memorandums, those dealing with tax issues, which are the most flexible ones".
Before leaving them to dine on Wednesday, May called for cooperation.
Angela Merkel, Emmanuel Macron and the leaders of Belgium and Luxembourg surprised late-night drinkers by dropping by a Brussels bar for beer and fries after an evening of summitry on Brexit with British Prime Minister Theresa May.
But the Prime Minister said she does not expect any extension of the so-called "transition" to Brexit to be needed, because she still hopes to conclude a deal on the UK's future trade and security relationship with the European Union by its scheduled end-date of December 2020.
Leo Varadkar reiterated Ireland's position on the backstop, which he said must be legally operable and would prevent a hard border emerging between Northern Ireland and the Republic.
Pro-EU politicians, meanwhile, said the transition period proposal was another sign of May's weak bargaining hand and an attempt to stall for time. Both sides agree there must be no hard border that could disrupt businesses and residents on both sides and undermine Northern Ireland's hard-won peace process.
Prime Minister Theresa May confirmed Thursday (Oct 18) that Britain would consider extending the transition period after Brexit for a few months if needed to agree a new trade deal with the EU. Agreement on such an extension could help break the deadlock on the talks.
Politics matters. And an extension to the transition period clearly has its opponents. "That's a good idea", European Commission chief Jean-Claude Juncker said. "I think that this is giving us some room to prepare the future relation in the best way possible", he told reporters after the summit.
"Where there is a will there should be a way", she said on Thursday. But even an extension will not get rid of the EU's insistence that such a backstop must be agreed to secure a deal. "Where there's a will, there should be a way, and normally there is a way".More news: Colbert mocks Trump for finally admitting journalist Jamal Khashoggi is likely dead
"The answer is yes", Barnier said when asked on France Inter radio if the Irish border issue could cause the negotiations to collapse. "I believe we need a deal".
European Union leaders have recently suggested that the transition period, now due to end in December 2020, could be extended by a year to provide more time for a trade deal to be forged that would make the backstop unnecessary. May spoke of "working intensively over the next days and weeks" to achieve agreement that avoids a no-deal departure from the bloc for Britain on March 29 that could create chaos at the borders and in the economy.
EU Council President Donald Tusk said the summit also left him more optimistic than he'd been after a bad-tempered meeting last month and a negotiating crisis on Sunday.
Mr Tusk added: 'I feel we are closer to the final solutions and the deal.' But Mrs May looked an isolated figure after a photo emerged of European Union leaders, including Germany's Angela Merkel and France's Emmanuel Macron, having a drink without her on Wednesday. He acknowledged that "it may be a more emotional impression than a rational one, but emotions matter, also in politics".
The "temporary" arrangement would be "so favourable" to the European Union, and "so injurious to Britain", that Brussels would lose interest in further talks.
The UK prime minister is under pressure to break key Brexit promises in order to get a deal.
A senior United Kingdom official stressed that the Prime Minister is not herself proposing any extension to the period already agreed, and declined to say how many months she regarded as the maximum she would consider.
The transition - during which the United Kingdom would remain in the single market and customs union and subject to EU rules - is meant to provide time for authorities and officials to prepare for new arrangements following the official date of Brexit in March 2019.
Britain officially is to leave the bloc in March and to have agreed to an exit deal well before then, but London and Brussels previously had agreed there would be a transition period to conclude at the end of 2020, by which time both sides hope some kind of trade agreement also would have been concluded.