British Prime Minister Boris Johnson has promised to take the United Kingdom out of the European Union on October 31, with or without a follow-on agreement to maintain orderly economic ties with its former partners.
Labour leader Jeremy Corbyn said he is "deeply concerned" about the negotiations and ruled out his party backing a deal under Mr Johnson's reported terms.
French Finance Minister Bruno Le Maire remains optimist, telling Europe 1 radio on Wednesday that there is a "glimmer of hope" that a Brexit deal can be reached before Britain's scheduled departure at the end of October.
"The 31st of October is still a few weeks away and there is a possibility of another summit before that if we need one".
"I can confirm, as the prime minister has repeatedly set out, that firstly the government will comply with the law and secondly will comply with the undertakings given to the court in respect of the law", Barclay told a committee of lawmakers.
But parliament has passed a law saying Britain cannot leave without an agreement, and Johnson has not explained how he can get around that.
Mr Johnson's alternative for replacing the backstop is thought to be a dual customs arrangement which would see Northern Ireland subject to European Union tariffs on goods, but de facto remain within the UK's customs jurisdiction.
This is expected as Irish Prime Minister Leo Varadkar said that there were "many issues" to be resolved before a Brexit agreement could be reached.
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Both sides were hoping that after more than three years of false starts and sudden reversals, a clean divorce deal for Britain leaving the bloc might be sketched out within the coming hours.
Reports that the last-ditch talks to seal a Brexit deal - to be approved by a summit of European Union leaders in Brussels on Thursday and Friday before Britain is due out on Oct.31 - hit sterling and stocks in London.
Mr Johnson is anxious to get a deal agreed before Saturday, when legislation requiring him to seek another Brexit delay kicks in.
More intense talks resumed this week after Britain softened its stance on the customs status of its province Northern Ireland in order to clinch an accord before the summit.
Britain's plan to leave the European Union, which has only ever added new member states, has compounded problems for a bloc torn by euroscepticism and economic disparities.
That greatly raised the group's profile and also brought a windfall in government funding for Northern Ireland.
The developments come as negotiators stepped up efforts to work out a way to break the deadlock over the Irish backstop, the contingency measure to prevent a hard border on the island of Ireland that is seen as the key factor in the talks.
Mr Donohoe said: "America's influence in Northern Ireland has always been very important, and will continue to be really important". But Northern Ireland's Democratic Unionist Party, the party that props up Johnson's minority Conservative government, strongly opposes any measures that could loosen the bonds between Northern Ireland and the rest of the United Kingdom.