British Prime Minister Boris Johnson has said he hoped the European Union would "see sense" and agree a post-Brexit trade deal.
He said all the bloc needed to do was recognise Britain's right to sovereignty.
Speaking in the House of Commons he said: "Every hope I have (is) that our friends and partners across the Channel will see sense and do a deal.
"And all that that takes is for them to understand that the UK has a natural right, like every other country, to want to be able to control its own laws and its own fishing grounds."
Earlier, the President of the European Commission said there is a narrow path to a post-Brexit trade agreement.
Ursula von der Leyen told MEPs this morning: "I cannot tell you whether there will be a [Brexit] deal or not, but I can tell you there is a path to an agreement. The path may be very narrow but it is there."
The commission president said there was a responsibility on both sides to keep negotiating and that despite agreement having been reached on most issues, "this is now a case of being so close and yet being so far away from each other".
With less than three weeks to go before the transition period ends and EU law ceases to exist in the UK, negotiators are still working on the twin issues of the level playing field, or fair competition, and fisheries.
Ms von der Leyen said outstanding issues around governance, or how to settle disputes, had "largely been resolved."
"As things stand, I cannot tell you whether there will be a deal or not. But I can tell you now that there is a path to an agreement. The path may be very narrow but it is there", President of the European Commission, Ursula von der Leyen told the European Parliament. #brexit pic.twitter.com/nnbvWRj2FY— RTÉ News (@rtenews) December 16, 2020
She said the "architecture" of a solution on the level playing field rested on the twin pillars of state subsidies and how both sides will approach the issue of labour, social and environmental standards.
She said both sides had made progress on state aid based on common principles, guarantees of domestic enforcement and the possibility to "autonomously" remedy the situation where needed.
This would involve both sides being able to take action through tariffs or other measures if there were distortions of trade.
She told the European Parliament: "We have agreed a strong mechanism of non-regression. That's a big step forward, this is to ensure our common, high labour, social and environmental standards will not be undercut."
Ms von der Leyen said fisheries remained "very difficult".
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"In all honesty it sometimes feels that we will not be able to resolve this question, but we must continue to try and find a solution, and it is the only responsible and right course of action.
"We do not question the UK's sovereignty in its own waters, but we ask for predictability and stability for our fishermen and our fisherwomen."
Ursula von der Leyen insists she is asking for "stability and predictability for EU fishermen and fisherwomen" with regards to a Brexit deal. I Read more: https://t.co/9HF3eMeCe1 pic.twitter.com/AZkzr56bfB— RTÉ News (@rtenews) December 16, 2020
The commission president appealed to the European Parliament to show flexibility in the coming days, given the potential difficulties in ratifying a treaty on time.
"The next days are going to be decisive. 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," she said.
A UK source told Reuters progress had been made but the two sides remained very far apart on key areas.
Ms von der Leyen and European Council President Charles Michel were among those speaking at the European Parliament this morning. MEPs are discussing the results of the EU summit on 10-11 December.
The main topics on the agenda were the EU's long-term budget, the recovery package, the Covid-19 vaccine, as well as the 2030 target to combat climate change.