The EU on Thursday put the onus on Britain to compromise on their new economic partnership or be ready for trade disruptions in less than 80 days.
The UK said it was "disappointed" with the bloc's stance.
British Prime Minister Boris Johnson will respond and set out his approach to the talks on Friday, his Brexit negotiator said.
Wearing face masks and keeping their distance amid a European surge in Covid-19 infections, the EU leaders meeting in Brussels gave more time for talks with Britain on a new trade pact before the year ends.
"We are concerned by the lack of progress and we call on the UK to make the necessary moves," European Council President Charles Michel said.
The bloc wanted an accord but not at any price, and it was ready for an abrupt split from 2021 as well, Mr Michel said.
Britain's Brexit negotiator, David Frost, tweeted that he was disappointed.
"Also surprised by the suggestion that to get an agreement, all future moves must come from UK," Mr Frost said.
Britain left the EU in January and during a transition period, they have been locked in complex negotiations to keep €1 trillion ($1.17tn) worth of annual trade free of tariffs or quotas from 2021.
Talks have narrowed gaps on issues from social welfare to transport, but a deal has so far been prevented by disagreement on fair competition, dispute resolution and fisheries, which is particularly important to France.
"In no case shall our fishermen be sacrificed for Brexit," said the French President, Emmanuel Macron.
"If the right terms can't be found at the end of these discussions, we're ready for a no-deal for our future relations."
With businesses and markets increasingly nervous as the deadline nears, EU leaders stressed the unity of the 27-nation bloc.
"We want a deal but obviously not at any price," said German Chancellor Angela Merkel.
"It has to be a fair agreement that serves the interests of both sides. This is worth every effort."
Ireland, the EU member most exposed to any no-deal Brexit, said a smooth transition between the world's sixth-largest economy and biggest trading bloc was even more essential given the economic havoc of the Covid-19 crisis.
"We still can get this resolved within the timeframe available to us," Irish Prime Minister Micheal Martin said.
The pandemic has thrust Europe into recession and many nations are tightening restrictions again to battle a second wave of infections as winter looms.
The coronavirus upset the meeting when the President of the European Commission, Ursula von der Leyen, left abruptly to go into precautionary isolation after one of her staff tested positive.
Given the economic malaise and global instability, it would be "crazy" if the two sides failed to agree on a deal, Dutch Prime Minister Mark Rutte said.
Many in financial markets expect a limited deal by early November, although after more weeks of drama.
The EU has warned it would not leave fishing rights to be settled last and stressed they must be part of a wider deal with issues such as energy ties, where London has a weaker hand.
The sides are also far apart on fair competition protection covering social, labour and environment standards, and state aid.
Britain wants to regulate its own corporate subsidies freely in the future, while the EU wants joint rules.
Otherwise, the bloc says Britain cannot have free access to its single market of 450 million consumers.