Ministers will resume efforts later to secure legally-binding changes to Theresa May's Brexit deal that might get MPs' backing in a week's time.
Brexit Secretary Stephen Barclay and Attorney General Geoffrey Cox will meet EU officials in Brussels in search of guarantees over the backstop plan to avoid border checks in Ireland.
Mr Cox has dismissed reports he has given up on securing a firm end date to ensure the UK is not stuck.
MPs will vote on the deal by 12 March.
The UK is currently scheduled to leave the European Union on 29 March.
If MPs reject the withdrawal agreement for a second time, they will have the opportunity to vote on whether to go ahead in just over three weeks' time without any kind of negotiated deal.
If they decide against, they will then have a vote on whether to extend negotiations and push the date of departure back by several months.
Separately, Scottish and Welsh politicians have joined forces to call for Brexit to be delayed in the first joint motion passed by the Scottish Parliament and Welsh Assembly in 20 years.
Leading Brexiteers are hoping Mr Cox will be able to change his legal advice to satisfy them that the backstop - a controversial plan which will see the UK aligned with EU customs rules until the two sides' future relationship is agreed or alternative arrangements worked out - will not endure indefinitely.
They have set a number of tests for the government's chief law officer and other ministers ahead of next week's votes.
Foreign Secretary Jeremy Hunt told BBC Radio 4's Today programme that signals from the EU were "reasonably positive" but there was "still a lot of work to do".
"Time is very short, but what I would say compared to where we were a month ago the situation has been transformed," he said.
"We need substantive changes that would allow the attorney general to change his advice to the government that says that at the moment, theoretically, we could be trapped in the backstop indefinitely.
"And I think the EU understands that we need that change."
Michael Tomlinson, one of an eight-strong group of Conservative MPs who will scrutinise what is brought back from Brussels, said only significant changes to the backstop would do.
"We support the prime minister in seeking treaty-level changes," he said after the group's first meeting on Monday.
A "proper analysis" of any new text would be needed to allow them to "form a judgement", he added.
BBC political editor Laura Kuenssberg said the group of Eurosceptics, who are also lawyers, will "pore over whatever Cox gets from Brussels", adding: "They will ultimately make a political call. The crucial bit for government is for the attorney general to feel he has enough to go on to change his legal opinion on the backstop."
Irish prime minister Leo Varadkar has said talks were continuing in Brussels, but maintained that the only "workable" solution so far had been the backstop proposed in the withdrawal agreement.
He said the Republic of Ireland will have to have "difficult discussions" with the EU and UK on how to avoid a hard border and protect the single market and customs union in the event of no deal.
Mr Cox took to Twitter on Monday after newspaper reports suggested he had turned his attention away from the concrete "freedom clause" demanded by many MPs to assurances that the backstop would fall away if talks on a future relationship break down.
He said while some of the reporting was accurate, "much more of it isn't". He added: "Complex and detailed negotiations cannot be conducted in public."
Meanwhile, Mr Barclay has written to EU negotiator Michel Barnier on protecting UK and EU citizen's rights after Brexit, following government support in Parliament for an amendment from Tory MP Alberto Costa.
In the letter, he said the government's position was that the withdrawal agreement provided "the best way of providing confidence to citizens".
But, he said given their "shared commitment to protecting the rights of citizens in all scenarios", he would welcome Mr Barnier's views on the proposal to ring-fence rights.
Mr Barclay added that more than 130,000 applications from EU nationals for settled status in the UK after Brexit have already been granted by the Home Office.
Environment minister George Eustice, who quit his job in order to oppose attempts to delay Brexit, has been replaced by Robert Goodwill, the MP for Scarborough and Whitby.