Johnson's Brexit Secretary, Stephen Barclay, got a warm welcome from European Union negotiator Michel Barnier before they started nearly two hours of talks Friday around breakfast. Barnier's meeting with ambassadors was still going on, but officials with knowledge of the talks said that the 27 other European Union countries had responded positively.
'Of course there is no guarantee of success and the time is practically up but even the slightest chance must be used'.
European Council President Donald Tusk said he has received "promising signals" that a Brexit deal is possible, after the leaders of the United Kingdom and Ireland said they could see a pathway to a potential agreement.
But the details of Mr Johnson's concessions are not yet known.
"You need vigilance, determination and patience", following his meeting with the UK's Brexit Secretary Stephen Barclay.More news: GM Boosts Contract Offer
Mr Barclay and Mr Barnier were dispatched after the two prime ministers held face-to-face discussions in the Wirral on Thursday, prompting the leaders to "see a pathway" to a possible agreement.
In a statement, the European Commission said: "The EU and the United Kingdom have agreed to intensify discussions over the coming days".
"I have received promising signals from [Varadkar] that a deal is still possible", he noted.
The softer mood music after Mr Johnson's meeting with the Taoiseach followed an intensive few days which saw an acrimonious war of words explode and the talks appear close to collapse.
Anonymous Downing Street sources accused Mr Varadkar of backtracking on previous commitments to try to find a deal, and of refusing to negotiate.More news: Federal Appeals Court Rejects Trump's Appeal of Subpoena for His Tax Returns
The 27 countries staying in the European Union after Britain leaves gave the go-ahead yesterday for their chief negotiator to hold another round of intense and secret negotiations with London in a bid to secure a deal, two senior diplomatic sources said.
On Wednesday, Mr Barnier told the European Parliament there was still no basis for a fresh agreement.
Johnson has vowed Britain will end its five-decade membership of the European Union on October 31, with or without agreeing exit terms.
In the event of a no-deal Brexit, regions and sectors in Ireland which are more reliant on trade with Britain and which are more vulnerable to the imposition of tariffs and non-tariff barriers, particularly sectors such as agriculture, food and the broad SME (small and medium-sized enterprises) sector, are likely to be more adversely affected, he said.
Whatever the outcome of the "tunnel" talks and next week's summit, United Kingdom lawmakers will be recalled on October 19, a Saturday, for an emergency parliamentary session.
Without a deal, Mr Johnson will face demands from opposition parties to comply with the so-called Benn Act which would require him to request a three-month Brexit delay if there is no agreement by October 19.More news: Younger generations more likely to quit job for mental health reasons
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