The UK has been given 48 hours to table fresh proposals to break the Brexit impasse, EU diplomats have been told.
EU officials said they would work non-stop over the weekend if “acceptable” ideas were received by Friday to break the deadlock over the Irish backstop.
The UK has said “reasonable” proposals to satisfy MPs’ concerns about being tied to EU rules had already been made.
There have been few visible signs of progress ahead of Parliament’s second vote on the Brexit deal next Tuesday.
MPs emphatically rejected the terms of withdrawal negotiated by Theresa May in January.
If they do so again, they will get to choose between leaving without a deal or deferring the UK’s exit date from the EU beyond the scheduled 29 March.
The PM is seeking legally-enforceable changes to the backstop – an insurance policy designed to prevent physical checks on the border between Northern Ireland and the Republic of Ireland.
Mrs May is pinning her hopes on getting changes to it that will prevent the UK from being tied to EU customs rules if no permanent trade deal is agreed after Brexit.
Critics say that – if the backstop were used – it would keep the UK tied to the EU indefinitely.
Negotiations between British ministers and the EU officials over the past 24 hours have been described as “difficult”, with the EU insisting there has been no breakthrough.
Diplomats from the 28 member states were told on Wednesday that Mrs May could meet European Commission President Jean-Claude Juncker on Monday if progress was made.
But the BBC’s Europe reporter Adam Fleming said talk of a 48-hour deadline for new proposals and a weekend of negotiations was “a notional timetable” and that more flexibility could be possible.
Attorney General Geoffrey Cox, who is leading the UK team, has conceded that negotiations are at a sensitive point and the exchanges have been “robust”.
Mr Cox, who will take questions from MPs on Thursday, has played down reports he has abandoned hopes of getting the EU to agree to a firm end date to the backstop or some kind of exit mechanism – key demands for many Tory Brexiteers.
The government has suffered the first of what are expected to be a number of defeats in the Lords on a key piece of post-Brexit legislation.
Peers voted to amend the Trade Bill to require the government to get Parliament’s approval for its negotiating strategy ahead of the next phase of talks on future relations with the EU.
Meanwhile, Labour leader Jeremy Corbyn has met Conservative MPs who back a close, Norway-style relationship with the EU after Brexit.
He discussed the idea of a “Common Market 2.0” trade-focused model with former ministers Nick Boles and Sir Oliver Letwin.
Mr Boles said the goal was to reach a cross-party compromise to ensure the UK left the EU but in a manner which protected its economic interests.