The EU’s lead Brexit negotiator has rejected Boris Johnson’s demands for the Irish backstop to be scrapped.
Michel Barnier said the backstop – intended to avoid a hard border on the island of Ireland – was the “maximum flexibility” the EU could offer.
Mr Johnson has previously told the EU the arrangement must be ditched if a no-deal Brexit was to be avoided.
Meanwhile, the PM has told rebel Tories they face a “fundamental choice” of siding with him or Jeremy Corbyn.
The backstop is part of the withdrawal agreement negotiated between Brussels and former Prime Minister Theresa May, which has been rejected by Parliament three times.
If implemented, it would see Northern Ireland staying aligned to some rules of the EU single market, should the UK and the EU not agree a trade deal after Brexit.
“In this sense, the backstop is the maximum amount of flexibility that the EU can offer to a non-member state.”
Mr Barnier also said he was “not optimistic” about avoiding a no-deal Brexit, but “we should all continue to work with determination”.
He added: “The EU is ready to explore all avenues that the UK government may present and that are compatible with the withdrawal agreement.”
Mr Johnson says he wants to leave the EU on 31 October with a deal, but it is “do or die” and he is willing to leave without one rather than miss the deadline.
That position has prompted a number of opposition MPs to come together to try to block a possible no deal.
MPs opposed to a no-deal Brexit are expected to try and seize control of the Parliamentary agenda this week to push through legislation that would force the PM to seek a Brexit extension beyond 31 October.
But Mr Johnson has warned Tory MPs who are considering lining up with opposition groups that they risk plunging the country into chaos.
“Are you going to side with those who want to scrub the democratic verdict of the people – and plunge this country into chaos.
On Saturday, demonstrations were held across the UK in response to Mr Johnson’s plans to suspend Parliament in the run-up to Brexit.
The prime minister, who announced the move on Wednesday, said it would enable the government to bring forwards new legislation.
But the decision prompted an angry backlash from politicians and opponents of a no-deal Brexit.
But Chancellor Sajid Javid defended the decision, adding: “It’s right because we are focusing on the people’s priorities.”
If the prorogation happens as expected, Parliament will be closed for 23 working days.
MPs have to approve recess dates, but they cannot block prorogation.