The UK prime minister Theresa May, the EU chief executive Jean-Claude Juncker and his chief Brexit negotiator Michel Barnier will meet on Monday in what will mark the "absolute deadline" for London to deliver "sufficient progress" in its divorce offer as set by European Council president Donald Tusk.
But the talks will be held against a hardline backdrop the EU laid out on Frday, when Mr Tusk said the bloc will refuse Britain's demand for talks on a post-Brexit transition and future trade pact if Ireland is not satisfied with London's offer on border arrangements with Northern Ireland.
Mr Tusk, who will chair a crunch summit of European Union leaders on the issue in two weeks, was speaking after meeting the Irish prime Minister Leo Varadkar in Dublin.
"Before proposing guidelines on transition and future relations to the leaders, I will consult the taoiseach [Mr Varadkar)] if the UK offer is sufficient for the Irish government," Mr Tusk said.
"Let me say very clearly: if the UK offer is unacceptable for Ireland, it will also be unacceptable for the EU. I realise that for some British politicians this may be hard to understand," he said.
"This is why the key to the UK’s future lies - in some ways - in Dublin, at least as long as Brexit negotiations continue."
After speaking with Mr Tusk, Mr Varadkar added: "The UK must offer credible, concrete and workable solutions that guarantee that there will be no hard border, whatever the outcome of the negotiations and whatever the future relationship between the EU and the UK is."
"The next couple of days will be crucial," he said.
A former Polish prime minister, Mr Tusk noted that he had given Mrs May a deadline of Monday to make a "final offer" on the Irish border before leaders decide whether there is "sufficient progress" on a divorce settlement to merit opening talks on the future relationship.
He insisted there could be no division between the other 26 EU members and Ireland: "The EU is fully behind you and your request that there should be no hard border on the island of Ireland after Brexit," he said. "The Irish request is the EU’s request."
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He added: "The UK started Brexit, and now it is their responsibility to propose a credible commitment to do what is necessary to avoid a hard border."
Although Ireland said on Friday a breakthrough on the future of the Irish border after Brexit remained "doable" before the key EU summit in two weeks' time, the negotiating teams are "not there yet", the Irish foreign minister Simon Coveney said.
If London meets the three key EU conditions on its financial bill for leaving, the rights of expatriate citizens and the border, then leaders could give a green light to trade talks at the summit on December 14-15.
"The UK must offer credible, concrete and workable solutions that guarantee that there will be no hard border ... whatever the future relationship between the EU and the UK is," Mr Varadkar said.
"I'm an optimist by nature ... However I'm also prepared to stand firm with our partners if need be ... if the UK offer falls short."
Before it can sign off on the first phase, Dublin wants Mrs May to spell out in writing how she intends to make good on a commitment to avoid turning the clock back to a border of customs and security checks. It says the best way to do so is to keep regulations the same on both sides of a border that will be the UK's only land boundary with the EU after Brexit.
Mrs May's government has said Britain will leave the EU's single market and customs union but wants the Irish border to remain open, a stance that EU officials say is contradictory.
