British Prime Minister Boris Johnson has told French President Emmanuel Macron that the EU should not believe Brexit will be delayed beyond the October 31 deadline.
Mr Macron earlier told Mr Johnson that the EU would decide by the end of the week whether a Brexit deal was going to be feasible.
The proposals tabled by Mr Johnson last week were quickly dismissed by Brussels and the French leader said it was up to Britain to reconsider before the EU summit on October 17 and 18.
Mr Johnson spent the weekend speaking to EU leaders Mr Macron and Portugal’s Antonia Costa, and will probably travel to the continent this week.
In a call on Sunday, Mr Macron told the British leader that talks could only be advanced through the EU’s chief Brexit negotiator Michel Barnier, who refused to meet him for talks.
“Boris Johnson presented his latest proposals,” an official at the Elysee Palace said of the conversation.
“The president told him that the negotiations should continue swiftly with Michel Barnier’s team in coming days, to evaluate at the end of the week whether a deal is possible that respects European Union principles.”
Mr Johnson’s proposals involve the return of a Customs border on the island of Ireland and a Democratic Unionist party veto on Northern Ireland staying in the EU’s single market for goods, to avoid checks on the border.
Apart from the EU's rejections, the British leader is facing domestic obstacles to his preferred Brexit.
On September 9, MPs passed the Benn Act, which requires Mr Johnson to ask for an extension to the deadline to avoid a no-deal Brexit on October 31.
But on Sunday evening, The Telegraph reported that Mr Johnson would likely try to sidestep the act and is considering legal action to ensure Britain could leave the bloc this month without a deal.
The report, quoting government sources, said Mr Johnson could give evidence before the British Supreme Court to try to persuade judges against forcing him to ask the EU for a delay.
He is likely to lose this appeal, but his aim may be to deflect the blame of not meeting the Brexit deadline, so he could strengthen his hand in an imminent general election.
It is likely that the British public will be asked to go to the polls if the UK has not left the EU by October 31.
The next week is set to be a busy one for Mr Johnson.
Irish leader Leo Varadkar said on Saturday that he wanted to arrange a meeting with him, stressing that time was tight for London to go further with the new Brexit proposals it presented this week.
There were signs that talks between Britain and the EU were breaking down at the weekend, when Mr Barnier said on Saturday that Mr Johnson's government would bear the full responsibility for a no-deal Brexit.