There is now a "very narrow path" to a Brexit deal and the next few days will be "decisive", an EU chief has announced.
Ursula von der Leyen told MEPs negotiations were "so close and yet so far" from completion on the two outstanding issues - the level playing field of how far Britain follows EU rules, and fisheries.
But she said a UK-EU trade deal was the "unfinished business of this year" and negotiators are "working day and night, sometimes against all odds".
She said while discussions on fisheries are still "very difficult" and it feels sometimes they will not be resolved, issues linked to governance - which was a third sticking point - "now have largely been resolved".
The European Commission President told the European Parliament in Brussels: "As things stand, I cannot tell you whether there will be a deal or not.
"But I can tell you that there is a path to an agreement now. The path may be very narrow but it is there. And it is therefore our responsibility to continue trying.
"The good news is that we have found a way forward on most issues. But this is now a case of us being so close, and yet being so far away from each other.
"Because two issues still remain outstanding: the level playing field and fisheries."
She added: "The next days are going to be decisive. And I know I have said this before and I know deadlines have been missed time and again."
"The clock puts us all in a very difficult situation - not least this Parliament and its right to exercise democratic scrutiny and ratification."
Downing Street today said there had been some progress but a no-deal Brexit was still “the most likely outcome”.
Asked if MPs could sit on New Year's Eve to pass a deal a spokesman said: “I’m not going to get into hypotheticals”.
It comes after talks were extended beyond a deadline of Sunday night in a last-ditch bid to reach a trade deal before EU rules end in the UK on December.
MPs are braced to sit in Parliament as late as Christmas Eve or even the week before Christmas and New Year to ratify a deal in the UK.
And the European Parliament has pencilled in a possible session just days before the cut-off date of December 31.
If no deal is agreed it will slap tariffs on January 1 on much of the UK's £660bn-a-year trade with the EU - pushing up food and clothes prices - and worsen chaos at the ports.
On the level playing field issue, Ms von der Leyen said: "Our aim is simply to ensure fair competition on our own market".
She said the UK and EU had agreed "a strong mechanism of non-regression" on standards to ensure UK rules don't undercut the EU in future, which is a "big step forward".
On fisheries, she said: "We do not question the UK's sovereignty on its own waters - but we ask for predictability and stability for our fisherman and our fisherwomen.
"And in all honesty, it sometimes feels that we will not be able to resolve this question.
"But we must continue to try finding a solution and it is the only responsible and right course of action."
