European Council President Donald Tusk and British Prime Minister Theresa May | Frederic Sierakowski/AFP via Getty Images Donald Tusk: No-deal Brexit ‘more likely than ever’ European Council president urges leaders to ‘remain hopeful’ because there is still goodwill in the negotiations.

A no-deal Brexit is "more likely than ever before," European Council President Donald Tusk warned in a letter to EU leaders Monday, a day after negotiations between Brussels and London hit a new wall.

Downing Street confirmed Monday that British Prime Minister Theresa May would accept an invitation from Tusk to address EU27 leaders ahead of a dinner Wednesday evening, during which they will discuss the state of play in the Brexit talks.

But Tusk's letter, ahead of that European Council summit, served to remind leaders of where they had hoped the Brexit process would be by now, and by implication the political leaps still required for a deal. "We wished for maximum progress and results that would lead to a deal in October," he wrote.

"As things stand today, it has proven to be more complicated than some may have expected," Tusk continued. "We should nevertheless remain hopeful and determined, as there is good will to continue these talks on both sides."

Still, he warned that the EU must prepare for the worst-case scenario. "Responsible as we are, we must prepare the EU for a no-deal scenario, which is more likely than ever before," Tusk wrote.

The sober tone of Tusk's note reflects deepening unease among EU officials over May's opposition to the EU's demand of an all-weather "backstop" that would prevent the recreation of hard border between Northern Ireland and Ireland.

The EU’s proposed backstop would effectively keep Northern Ireland inside of the bloc’s customs union as a way of drastically minimizing the need for checks on goods, including livestock and agricultural products, traveling between the U.K. and Ireland. London has objected, saying the EU’s plan would undermine the constitutional integrity of the U.K. by treating Northern Ireland differently and essentially creating an imaginary internal border in the Irish Sea.

Brussels insists that its proposed backstop is nothing more than a safeguard that is never intended to be used, but would protect the Good Friday peace agreement in the event that negotiations on the future EU-U.K. relationship last longer than expected, or perhaps break down.

In Brussels, May’s refusal to accept the EU version of the backstop is viewed not merely as a principled stand in defense of British sovereignty but also as a reflection of her continuing political weakness.

In his letter, Tusk urged the EU27 leaders to remain focused on reaching an accord that would provide for the U.K.'s orderly withdrawal.

"Let me be absolutely clear," Tusk wrote. "The fact that we are preparing for a no-deal scenario must not, under any circumstances, lead us away from making every effort to reach the best agreement possible, for all sides. This is what our state of mind should be at this stage. As someone rightly said: 'It always seems impossible until it's done.' Let us not give up."