Brexit deal? Boris Johnson and Irish leader Leo Varadkar 'can see pathway'

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British Prime Minister Boris Johnson's office says he won't resign but will cut his trip to the United Nations in New York short and return to the U.K. earlier than expected.

British Prime Minister Boris Johnson and his Irish counterpart Leo Varadkar had "constructive" talks in the Brexit proposal and agreed Thursday they can "see a pathway to a possible deal" following a last-ditch meeting aimed at finding a way for the United Kingdom to leave the European Union with an exit deal.

The two leaders believe a deal "is in everybody's interest," Downing Street said in a statement that seemed to give momentum to a meeting scheduled Friday between Brexit Secretary Stephen Barclay and EU's chief negotiator Michel Barnier.

BREXIT DEAL IS 'ESSENTIALLY IMPOSSIBLE' JOHNSON SAYS, IF EU STANDS BY TRADE DEMAND 

There are only three weeks to go before the U.K. is expected to leave the word's largest trading bloc though there have been concerns about how it will happen or whether it will happen at all.

Attempts to craft an exit deal have foundered over plans for the border between EU member Ireland and the U.K.'s Northern Ireland.

The currently all-but-invisible border underpins both the regional economy and Northern Ireland's peace process.

There was little of substance in Varadkar and Johnson's statement indicating a breakthrough or whether the "pathway" was near or far off.

Britain's Prime Minister Boris Johnson speaks to mental health professionals during his visit to Watford General Hospital, in Watford, on Monday. (AP)

The two agreed to “reflect” further on their discussions, which concentrated on the challenges of customs and consent. They also agreed to keep talking.

BREXIT PROPOSAL MET WITH SKEPTICISM BY EUROPEAN LEADERS WHO SAY THEY ARE 'STILL UNCONVINCED'

Under a U.K. proposal, there would have to be customs checks on some goods, though not on the border itself. The EU says any customs checks are unacceptable.

In recent days, Britain and the EU have traded ill-tempered barbs about who is responsible for the deadlock in talks.

After Johnson’s Downing Street office claimed EU intransigence had made it “essentially impossible” for the U.K. to leave with a deal, European Commission President Donald Tusk warned against playing a “stupid blame game.”

Irish Prime Minister Leo Varadkar grimaces during a press conference with Swedish Prime Minister Stefan Lofven in Stockholm, on Thursday. (AP/TT News Agency)

Varadkar and other EU leaders say Johnson, who took office in July, has repudiated the withdrawal agreement made with the bloc by his predecessor, Theresa May. That deal was rejected three times by Britain’s Parliament, largely because of lawmakers’ opposition to provisions to ensure an open Irish border.

Johnson insists the U.K. will leave the U.K. on Oct. 31, with or without a divorce deal.

However, many members of Britain’s Parliament are determined to prevent a no-deal Brexit, which economists say would plunge the U.K. economy into recession. Last month, they passed a law requiring the government to ask the EU for a delay if no divorce deal has been agreed by Oct. 19 — the day after a key summit of EU leaders in Brussels.

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Johnson says he won’t delay Brexit past Oct. 31 — but also will obey the law. It’s unclear how the two statements can be reconciled.

Parliament is expected to hold a rare Saturday sitting on Oct. 19 as lawmakers grapple with what to do next.

The Associated Press contributed to this report.