Boris Johnson is under pressure to concede more ground to Brussels as the price of agreeing a Brexit deal as negotiations reach a critical stage ahead of the looming deadline for the UK to leave the EU.
UK and EU officials will resume talks in the Belgian capital on Monday.
Time is rapidly running out to agree on a deal to put to EU leaders to sign-off on at their two-day summit starting on Thursday.
The EU's chief negotiator, Michel Barnier, said "technical-level" talks between officials over the weekend had proved "constructive".
But in a briefing to ambassadors of the remaining EU27 on Sunday, he said "a lot of work remains to be done" and that a “big gap” remains over customs arrangements between Northern Ireland and the Republic of Ireland.
The BBC has reported that the UK has dropped a demand that the deal should include a veto for the Stormont Assembly.
Updating about the Brexit negotiations today, the Prime Minister’s spokesman cautioned that there is still ground to be covered.
“The talks remain constructive but there is still a lot of work to do,” said the Number 10 spokesman.
Earlier, Mr Johnson told senior ministers that while a "pathway" to a deal could still be seen, there was "still a significant amount of work to get there".
In a Cabinet conference call, he said the UK still had to be prepared to leave on Halloween without a deal.
Leader of the House Jacob Rees-Mogg has said the government could achieve a no-deal Brexit by using European law.
"Theresa May got an extension not through UK law but through EU law and, until the 1972 European Communities Act is repealed, EU law is superior law in the UK," he said on BBC Radio 4’s Westminster Hour.
"And the Remainiacs all know that, because they know that it takes two to tango and any extension has to be agreed by the council."
The sticking point in the negotiations remains the issue of the Northern Ireland backstop, the mechanism intended to guarantee there is no return of a hard border with the Republic of Ireland.
Further Brexit delay?
It was reported there are doubts about the feasibility of Boris Johnson’s plan to replace the backstop, which was said to involve tracking goods as they move through Northern Ireland and then determining the tariff to be paid depending where they end up.
The concerns raised the prospect that negotiations could carry on after this week, with the possibility of an emergency EU summit at the end of the month to finally approve any 11th-hour agreement.
However, if Mr Johnson cannot get a deal by the weekend, he is required by law to seek a further Brexit delay, something he has vowed not to do.
Labour has warned that if necessary it will take action through the courts to force him to comply with the so-called Benn Act, which requires the prime minister to request an extension.
Either way, the stage is set for a major Commons showdown when Mr Johnson returns to Westminster for an emergency sitting of Parliament, the first on a Saturday in 37 years.
If he cannot get a deal, he is widely expected to blame MPs for cutting the ground from under him, laying the ground for a "people versus Parliament" general election.
If he is able to get an agreement, he may seek to rush through legislation to ratify it in time for the promised Halloween withdrawal date.
Some opposition MPs have signalled that they could support an agreement if there was a requirement to put it to the public in a confirmatory referendum.
However, Labour leader Jeremy Corbyn indicated he had little enthusiasm for the idea.
"I think many in Parliament, not necessarily Labour MPs but others, might be more inclined to support it (if there was a referendum) even if they don't really agree with the deal,” he said. “But I would caution them.”