BRUSSELS - Britain and the EU failed to strike a Brexit divorce deal during talks in Brussels on Monday but said they were "confident" of reaching an accord later this week.

British Prime Minister Theresa May and European Commission President Jean-Claude Juncker fell short of a breakthrough, despite encouraging progress on the thorny issue of the Irish border.

The EU says Britain must make sufficient progress on key divorce issues - Ireland, Britain 's financial bill for leaving the bloc, and the rights of EU nationals in Britain - to allow the opening of trade and transition talks at a summit on December 15.

"Despite our best efforts and the significant progress we and our teams have made in the past days on the remaining withdrawal issues, it was not possible to reach a complete agreement today," Juncker said at a joint news conference with May. "This is not a failure... I am very confident that we will reach an agreement in the course of this week."

Juncker, a former Luxembourg prime minister, said May was a "tough negotiator and not an easy one."

May said differences remained on a "couple of issues". "But we will reconvene before the end of the week, and I am also confident we will conclude this positively," May said.

The failure of the talks came despite EU president Donald Tusk saying just hours earlier that negotiators were "getting closer to sufficient progress" at the December summit, and that he was "encouraged" by a phone call with Irish Prime Minister Leo Varadkar. Tusk - who was to see May later in Brussels, and who cancelled a Middle East trip because of the "crucial" talks - said recently that Monday was the "absolute deadline" for an improved offer from London.

Irish broadcaster RTE said Britain was ready to keep the EU customs and single market rules for Northern Ireland in order to meet Dublin's insistence that Brexit should not bring back a "hard border" and threaten a peace process that ended decades of sectarian tensions.

Dublin's demands on the status of the border with British-ruled Northern Ireland have been the key stumbling block recently, with fears that the talks could even collapse amid tensions between the two neighbours.

But an angry reaction from the Northern Irish unionists who prop up May's minority Conservative government meant there was still no deal three hours later, and the meeting was put on hold while May made calls to try to win them over.

"We will not accept any form of regulatory divergence which separates Northern Ireland economically or politically from the rest of the United Kingdom," Democratic Unionist Party leader Arlene Foster said in a statement.

In a sign of the tensions within the United Kingdom caused by Brexit, the leaders of Scotland and Wales together with the mayor of London all called for similar deals to the one being considered for Northern Ireland. May, Brexit minister David Davis and the prime minister's Brexit adviser Olly Robbins attended the "working lunch" with Juncker, the EU Brexit negotiator Michel Barnier and Juncker's chief of staff Martin Selmayr.

The EU has demanded "sufficient progress" from Britain on the exit bill, citizens rights and Ireland in order to move on to talks on a post-Brexit transition period of up to two years, and on a future relationship including a trade deal.

Failure to do so this month could make the EU "rethink" whether an overall Brexit withdrawal deal is possible at all, Tusk has warned, raising the prospect of a chaotic exit with far-reaching economic effects.

After months of stalemate, London and Brussels have effectively reached a deal on the divorce settlement, reported to be 45 billion to 55 billion euros ($51 to $63 billion), and previously the most contentious issue.

Despite anger from Brexit supporters, they appear to have reached a compromise, with London increasing its offer but Brussels offering enough wiggle room for the British government to be able to present its own, lower figures to the public.

A deal is also close on the rights of more than three million Europeans living in Britain , though there is still disagreement over whether they would be protected by the European Court of Justice - a red line for Brexit supporters in Britain .