Luxembourg (CNN) Brexit talks have hit a wall.

Negotiations between the UK and the European Union broke up on Sunday without a deal, three days before a critical summit of European leaders that was intended to mark significant progress on a Brexit agreement.

The sticking point remains the thorny issue of the Irish border. The European Union wants the UK to agree a "backstop" or fallback position that would ensure an open border between Northern Ireland, which will be outside the EU, and the Republic of Ireland, which will remain an EU member state.

Britain's chief negotiator, Dominic Raab, made an unexpected visit to Brussels, Belgium, on Sunday for a meeting with his EU counterpart Michel Barnier, after which it was clear an impasse had been reached. "Despite intense efforts, some key issues are still open, including the backstop," Barnier wrote on Twitter.

UK Prime Minister Theresa May sought to downplay Sunday's talks as another setback, telling members of Parliament on Monday that "real progress" had been made, particularly on the issue of Northern Ireland, and that a Brexit deal was still "achievable."

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