LONDON — The British and Irish leaders were meeting today to discuss the Irish border — and mend fences — amid rising tensions between Britain and the European Union over Brexit.

British Prime Minister Theresa May was due to dine with Irish premier Leo Varadkar in Dublin to press her case for changes to Britain's divorce deal with the EU. Britain's Parliament rejected the agreement last month, largely over concerns about a provision designed to ensure an open border between the U.K.'s Northern Ireland and EU member Ireland.

Britain is due to leave the bloc on March 29, and the U.K.'s bid for last-minute changes has exasperated EU leaders, who insist the legally binding withdrawal agreement can't be changed.

Brexit tensions boiled over this week when EU Council President Donald Tusk wondered aloud what "special place in hell" might be reserved for those in Britain who had backed Brexit with no idea of how to deliver it. The comments enraged British Brexiteers, and May reprimanded Tusk for causing "dismay."

Tusk spoke ahead of talks between May and EU leaders on Thursday that both sides described as "robust."

Neither side moved from their entrenched positions, but they did at least agree to keep talking, with May and EU Commission President Jean-Claude Juncker saying they would meet again before the end of the month, after more talks between their officials.

The British and Irish attorneys general were meeting today to see if there is any common ground on the border provision, known as the backstop. It's a safeguard that would keep the U.K. in a customs union with the EU to remove the need for checks along the border until a permanent new U.K.-EU trading relationship is in place.

Britain has suggested the backstop could be altered by adding a time limit or a get-out clause. Both ideas have been rejected by officials in Brussels.

The impasse leaves Britain lurching toward a chaotic "no-deal" departure that could be costly for businesses and ordinary people in both the U.K. and the EU.

May is determined to win backing in Parliament for her deal, but many lawmakers want her to change course.

Britain's Parliament is set to hold a debate and votes Thursday on the next steps, giving lawmakers a chance to force May to tack toward a softer Brexit — if divided legislators can agree on a plan.

The main opposition Labour Party said this week that it could support a Brexit deal if May committed to seeking a close relationship with the EU after Britain leaves. But any such move would cost May the support of a big chunk of her Conservative Party.

Labour finance spokesman John McDonnell said "people have looked over the edge of a no-deal Brexit and it could be catastrophic for our economy."

"In the national interest we have got to come together to secure a compromise," he said.

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