The UK and EU have failed to reach an agreement to move to the next stage of Brexit talks, Theresa May has said.
The UK prime minister said differences remain on a "couple of issues".
She said talks would reconvene "before the end of the week" and she was "confident we will conclude this positively".
The BBC's Laura Kuenssberg said the deal had been "sunk" by the Democratic Unionist Party (DUP), which reacted angrily to reports of concessions on the Irish border issue.
Mrs May is understood to have broken off from talks with European Commission President Jean Claude Junker to speak to DUP leader Arlene Foster.
This was after Ms Foster had said her party "will not accept any form of regulatory divergence" that separates Northern Ireland from the rest of the UK.
"During the call it was made plain to the PM that the DUP had significant concerns about the deal being discussed that gave concessions to the Dublin government," the BBC's political editor said.
"I understand Foster told Theresa May that she would not be able to support such a deal. It's been suggested too that there are 20 or so Conservative MPs who had serious misgivings about the compromises that were understood to be on the table."
The UK was reportedly prepared to accept that Northern Ireland may remain in the EU's customs union and single market in all but name. The DUP's support is vital to the government being able to survive at Westminster and pass their Brexit legislation.
DUP leader Arlene Foster said her party would not accept any Brexit deal that "separates" Northern Ireland from the rest of the UK.
Her party's Brexit spokesman Sammy Wilson claimed Brussels has been trying to "bounce the prime minister into acceding to the shape of a deal they want" and many of her own backbenchers would not accept it.
He said the DUP objected to the form of words used in a draft document, which referred to "regulatory alignment" and "no regulatory divergence" between Northern Ireland the EU.
Both phrases were "simply EU speak for keeping Northern Ireland in the European market" and "in effect, part of the United Kingdom would be kept within the single market," he said.
Asked if the DUP would pull out of the confidence and supply agreement they have with the Conservative government in Westminster over this issue, he said: "I think that her (Theresa May) problem isn't going to be just with the DUP".
Speaking at a joint press conference in Brussels with Mr Juncker, Mrs May said: "We have been negotiating hard. And a lot of progress has been made. And on many of the issues there is a common understanding.
"And it is clear, crucially, that we want to move forward together. But on a couple of issues some differences do remain which require further negotiation and consultation."
The European Commission President said "it was not possible to reach complete agreement today" despite their "best efforts".
But he added: "I have to say that we were narrowing our positions to a huge extent today, thanks to the British prime minister, thanks to the willingness of the European Commission to have a fair deal with Britain.
"I'm still confident that we can reach sufficient progress before the European Council of 15 December.
"This is not a failure, this is the start of the very last round. I'm very confident that we will reach an agreement in the course of this week."
The EU says it will only recommend the start of talks about future trade arrangements when it deems "sufficient progress" has been made on three issues - the status of expat citizens, the "divorce" bill and the Northern Ireland border.
The UK has been set a deadline of this week to come forward with an improved offer on them, and hopes that the go-ahead for future talks will then be given at an EU leaders' summit on 14-15 December.
On the "divorce bill", the UK is understood to have recently increased its offer, which could be worth up to 50bn euros (£44bn).
On the issue of rights for the three million EU citizens in Britain, the UK has agreed that those who already have permanent residence will not have to pay to apply for settled status. Those making a first time application for the right to stay after Brexit, however, will face a charge - reportedly similar to the cost of applying for a passport.
Settled status will grant those who have spent five years in the UK equal rights on healthcare, education, benefits and pensions to British citizens.
Ministers have already suggested people legally resident in the UK before an as yet unspecified cut-off date will be allowed to stay and they want to make the process "as easy as renewing a driving licence".