LONDON — Britain’s faltering Brexit negotiations with the European Union got a lifeline on Thursday from an unexpectedly upbeat meeting between the leaders of Britain and Ireland, with both saying they could see “a pathway to a possible deal” to handle issues over Northern Ireland.
Meeting at a hotel outside Liverpool, England, Prime Minister Boris Johnson and Prime Minister Leo Varadkar discussed Britain’s proposal, which would take Northern Ireland out of the European customs union, along with Britain, but leave it aligned with many other European Union regulations.
“Both continue to believe that a deal is in everybody’s interest,” said a vaguely worded joint statement issued by the leaders. “They agreed that they could see a pathway to a possible deal.”
Still, for all the encouraging mood music, it was hard to judge whether Mr. Johnson and Mr. Varadkar had actually closed any gaps between them or were merely putting a diplomatic gloss on a negotiating effort that could fail before the Oct. 31 deadline for Britain’s departure from Europe.
They did not cite concrete progress on vexing issues, like customs checkpoints, which Ireland opposes, or the need for Northern Ireland’s assembly to approve the arrangement, which Britain is demanding. But neither did they repeat their past disagreements on these issues.
Speaking to reporters, Mr. Varadkar said he believed Britain and Europe could strike a deal before Oct. 31. But he acknowledged potential sticking points, saying, “there’s many a slip between cup and lip.” The normally voluble Mr. Johnson left without speaking to the press.
Mr. Varadkar said he hoped the meeting would give fresh momentum to parallel talks between Britain and the European Union, which had largely ground to a halt.
Diplomats said a meeting on Friday between the Brexit secretary, Stephen Barclay, and the European Union’s chief negotiator, Michel Barnier, would be crucial in determining whether talks intensify before a decisive summit of European leaders on Oct. 17.
Mr. Varadkar and Mr. Johnson met for two and a half hours and took a private walk around the grounds of the hotel, a manor normally used for upscale weddings. The atmospherics suggested that neither side was ready to give up, even though British officials have already pointed fingers at what they say are intransigent Europeans and the obdurate Irish.
Mr. Varadkar has been blunt about his objections to Mr. Johnson’s proposal, notably its requirement that Northern Ireland’s assembly — which has been suspended since its governing coalition collapsed in January 2017 in a sectarian dispute — be given a veto over the plan once every four years.
Before the meeting, Mr. Varadkar said, “Part of the difficulty at the moment, though, is the position of the U.K. government that Northern Ireland must leave the E.U. customs union and be part of the U.K. customs union, no matter what the people of Northern Ireland think. That’s their position at the moment, and that’s the one that’s of grave difficulty to us.”
British officials have floated various remedies to this problem, like having the major political parties in Northern Ireland — which represent both British unionists and Irish nationalists — sign on to an agreement, in lieu of the assembly. Another option is to impose a time limit on the deal, but set that date well in the future, giving Ireland hope that the north might never be divided from the south.
Finding a compromise on the issue of “consent” was expected to occupy most of Thursday’s meeting, though Mr. Johnson and Mr. Varadkar also said they had discussed the customs union. Of the two issues, consent is easier to resolve: Some of the details could be left until later, if the two sides reach agreement on basic principles.
The customs union is far harder: Britain argues it is necessary as a point of principle and to get a deal through Parliament. But it would require installing customs checks, although Britain insists such checks could be done away from the border between north and south.
Those are an obstacle for Ireland for practical reasons — they would interrupt the now seamless trade across the border — as well as a symbolic one — a hard border could threaten the peace that has prevailed since the 1998 Good Friday Agreement resolved years of sectarian strife in Northern Ireland.
The European Union and individual European leaders have steadfastly backed Ireland, generally echoing Mr. Varadkar’s objections. On Wednesday, Mr. Barnier told the European Parliament: “We’re not really in a position where we’re able to find an agreement.”
Mr. Johnson has threatened to leave the bloc without a deal if he cannot strike an agreement before Oct. 31. But that outcome seems less likely because of a Parliamentary law requiring the prime minister to ask the European Union for an extension by Oct. 19, if he does not achieve a deal.
As the days tick down, the British government has seemingly adopted a two-track strategy: Downing Street officials, usually anonymously, blame either the Irish or the European Union for torpedoing a deal, while the government quietly continues to look for ways to break the impasse.
Mr. Johnson’s meeting with Mr. Varadkar, held away from television cameras and the politically charged terrain of London or Dublin, was part of that second track. But British officials have also leaked a series of threats and warnings about what could happen if there is no deal by month’s end.