The UK has been urged to table fresh proposals within the next 48 hours to break the Brexit impasse. 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. It comes as Jeremy Corbyn has met with Tory MPs to discuss alternatives to the PM's deal.
The Labour leader held talks with ex-Tory minister Nick Boles and Sir Oliver Letwin, who favor a closer, Norway-style relationship with the EU.
He said he had discussed the so-called Common Market 2.0 option - which would see the UK remain in the EU's single market by staying part of the European Economic Area - but would not commit to backing it at this stage.
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.
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.
Mr Corbyn said he had agreed to meet Conservative MPs because he was adamantly opposed to a no-deal exit and he wanted to hear what their ideas and options are.
While Labour wanted an agreement encompassing a customs union, unhindered access to EU markets and legal protection of workers' rights, he said that what exact form that takes is subject to negotiation.
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.