British and EU negotiators on Tuesday scrambled to put together a draft text for a Brexit deal with just two days to go before a key European summit.
Both sides voiced cautious optimism that an outline agreement could be reached this week, but officials admitted time is tight.
And European leaders warned they would not let Britain use Northern Ireland as a back door to the single market.
EU chief negotiator Michel Barnier said a legal text must be on the table by Wednesday morning at the latest if it is to be signed off by leaders at the EU summit starting Thursday, in time for a special sitting of the British parliament on Saturday.
European diplomats said London has given ground on customs rules for Northern Ireland, but must go further quickly if a deal is to be done this month -- allowing Prime Minister Boris Johnson to fulfil his pledge to lead Britain out on October 31.
"The negotiating teams have made progress but it has been slow and they will have to make significant progress today if there is to be a deal that Michel Barnier can report on tomorrow to the EU capitals in advance of the leaders' summit," Irish Deputy Prime Minister Simon Coveney told reporters in Luxembourg.
As he arrived in Luxembourg to brief ministers from the other 27 EU states, Barnier struck a cautiously upbeat note.
"This work has been intense all along the weekend and yesterday because even if the agreement will be difficult -- more and more difficult to be frank -- it's still possible this week," he told reporters.
"Obviously any agreement must work for everyone -- the whole of the United Kingdom and the whole of the European Union. Let me add also that it is high time to turn good intentions into legal text."
Emmanuel Macron apparently shares Barnier's guarded optimism. An aide to the French president told reporters there was "positive momentum" behind the talks.
Downing Street said Johnson had called Macron and had a "constructive" and "good discussion". "We want to make progress towards securing a deal as soon as possible and we want to make progress ahead of the EU council on Thursday," a spokesman said.
But German Chancellor Angela Merkel outlined why EU officials are driving a hard bargain and hoping Britain will commit to a "level playing field" in post-Brexit trade and commerce.
"One thing is clear, Britain will develop into another competitor on the doorstep of Europe," she told industrialists. "And therefore the EU will be challenged to become more competitive and to assume geopolitical responsibility."
A European diplomat told AFP the "goal" was to get a draft text of a deal ready later in the evening Tuesday, but warned: "Time is running out."
Officials stressed that EU and UK negotiators would have to agree a draft text by Wednesday morning if it is to be ready to go before leaders at Thursday's summit, but EU sources insisted there was no "hard deadline" and talks could go on next week.
"The last moment is always a bit later than you think," one diplomat told AFP, suggesting that Brexit day would have to be postponed beyond the end of the month if talks are to succeed.
"I am sceptical that we will have a full agreement tomorrow on a legal text ... . the question is whether the work can be done in the next few days or whether it will take another two months."
- GLIMMER OF HOPE -
British Brexit Minister Stephen Barclay joined Barnier in Luxembourg in what was seen as a positive sign for the talks, and said "a deal is still very possible."
More than three years after Britain's 2016 referendum vote to leave, talks remain stuck on how to avoid customs checks on the border between British-ruled Northern Ireland and EU-member Ireland.
The EU has reservations about London's proposed customs arrangements and the role for Northern Ireland's Stormont assembly in giving consent to the plans.
"Johnson has modified his original proposals to the effect that he has clearly stated that there will be no customs border on the Irish border. He has also moved on how consent (in Northern Ireland) can be secured, but that depends very much on the details," a European diplomat told AFP, referring to the role of the Northern Irish provincial assembly.
"The UK proposal contained some steps forward, but not enough that the internal market will be protected," Dutch Foreign Minister Stef Blok said.
- NO NI BACKDOOR -If no deal is reached by Saturday, Johnson will fall foul of a British law demanding he ask the EU to postpone Brexit for a third time rather than risk a potentially disastrous "no deal" departure.
