BRUSSELS — Britain’s Brexit secretary and the top European Union negotiator met for surprise talks Sunday, and ambassadors from the 27 remaining EU countries gathered for a hastily scheduled discussion as the push for progress on a divorce deal quickened ahead of a vital summit.

British Brexit Secretary Dominic Raab’s office said in a statement that his rushed trip to Brussels to sit down with the EU’s Michel Barnier was necessary. EU leaders say significant progress is needed before Wednesday’s summit.

“With several big issues still to resolve, including the Northern Ireland backstop, it was jointly agreed that face-to-face talks were necessary,” Raab’s office said.

Britain and the EU are seeking a compromise position on the difficult Irish border question ahead of the summit that begins Wednesday. Three diplomats from different EU nations said the ambassadors’ meeting underscored that enough progress had been made to assess the situation.

One diplomat said that if an agreement takes shape, British Prime Minister Theresa May’s government would discuss it Monday.

The “Irish backstop” is the main hurdle to a deal that spells out the terms of Britain’s departure from the EU and future relationship with the bloc.

After Brexit, the currently invisible frontier between Northern Ireland and Ireland will be the U.K.’s only land border with an EU nation. Britain and the EU agree there must be no customs checks or other infrastructure on the border, but do not agree on how that can be accomplished.

The EU’s “backstop” solution — to keep Northern Ireland in a customs union with the bloc — has been rejected by Britain because it would require checks between Northern Ireland and the rest of the U.K.

The alternative — to keep the entire U.K. in a customs union until a permanent solution can be found — has angered pro-Brexit members of May’s government, who claim that approach would limit the country’s ability to strike new trade deals around the world.

The idea is also anathema to the Democratic Unionist Party, a Northern Ireland Protestant party that props up May’s minority government.

So even if May strikes a deal with Brussels, she will struggle to get it past her government and Parliament at home.

Raab’s predecessor, David Davis, wrote in the Sunday Times that May’s plans for some continued ties with the EU even after Britain leaves the bloc is “completely unacceptable” and must be stopped by her ministers.

May is struggling to build a consensus behind her Brexit plans ahead of a Cabinet meeting Tuesday that will be followed by Wednesday’s EU summit. If Davis’ call for a rebellion is effective, the Cabinet meeting is likely to be fractious.

Davis and former Foreign Secretary Boris Johnson resigned from May’s Cabinet this summer to protest her Brexit blueprint. While all three are in the ruling Conservative Party, the two men have become vocal opponents of May’s plan, saying it would betray the Brexit vote and leave Britain in a weakened position.

May also faces obstacles from the Democratic Unionist Party in Northern Ireland.

DUP leader Arlene Foster remains opposed to any Brexit plan that would require checks on goods traveling between Northern Ireland and Britain, as some EU leaders have recommended as part of a backstop.