Following the two-hour meeting, Mr Barnier was given the green light by European Union ambassadors for the pace to be stepped up.
"The EU's position remains the same: there must be a legally operative solution in the Withdrawal Agreement that avoids a hard border on the island of Ireland, protects the all-Ireland economy and the Good Friday (Belfast) Agreement in all its dimensions and safeguards the integrity of the single market". But Mr Tusk tempered this by saying: "Of course, there is no guarantee of success and the time is practically up".
The pound has climbed against the pound since Thursday's meeting between Irish prime minister Leo Varadkar and Boris Johnson.
Donald Tusk handed Boris Johnson a last-minute reprieve after talks with Leo Varadkar raised the prospects of a Brexit deal, but he warned the United Kingdom still has not presented a "workable, realistic proposal".
He added: "Brexit is like climbing a mountain".
Following his "technical" discussion with Mr Barclay in Brussels, Mr Barnier told reporters: "Be patient".
Dramatic progress could lead to the start of so-called intensive "tunnel" negotiations in the coming days, ahead of the crunch European Union heads of government summit. "I think it's possible for us to come to an agreement, to have a treaty agreed.by the end of October", he said.
Prime Minister @BorisJohnson meets Irish Taoiseach @LeoVaradkar to discuss the UK's Brexit proposals. "There's many a slip between cup and lip", he warned.
He refused to be drawn on any "concessions" made by either side, while UK Government sources would not comment on Irish press reports suggesting "significant movement" by the UK.
A short while later, Mr Barnier hailed the "constructive" talks with Mr Barclay. Downing Street is believed to have privately shared a proposed compromise with negotiators in Brussels.
Mrs. Foster went on to say that anything concerning Northern Ireland and Brexit could only be considered as credible if it commands cross community support from both unionists and nationalists.
The PM has said that, while he will abide by the law, he is determined to leave on the Halloween deadline of October 31 come what may.
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.
"It's a tunnel with a very small light at the end of it", one of the diplomats said, indicating there was not too much hope on the European Union side that a divorce deal could be sealed before the end of the month.
Should any new deal be reached between the European Union and United Kingdom, it will still have to be approved by MPs in Parliament.
A DUP source said, however, it was not opposed to a post-Brexit customs partnership: "Provided it doesn't mean that Northern Ireland is excluded from being able to participate in new trade deals, we could be supportive".
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