Talks between Britain's prime minister Boris Johnson and EU chief Ursula von der Leyen - aimed at breaking the Brexit trade talks deadlock - ended without agreement.
A senior No 10 source said "very large gaps remain" but negotiations will continue with a "firm decision" on the prospects of a deal by Sunday.
Von der Leyen said in a statement that the two sides were "far apart".
The Brussels dinner, also attended by negotiators Michel Barnier and Lord Frost, lasted about three hours.
The UK side said there had been "a frank discussion about the significant obstacles which remain in the negotiations".
"Very large gaps remain between the two sides and it is still unclear whether these can be bridged," the No 10 source said.
They added the two sides had instructed their respective negotiators to resume their work on Thursday and that the PM did "not want to leave any route to a possible deal untested".
Von der Leyen said the discussions had been "lively and interesting", and the two sides fully "understand each other's positions" but conceded they "remain far apart".
The BBC's Laura Kuenssberg said the evening had "plainly gone badly" and the chances of the UK leaving the post-Brexit transition period at the end of the year without a firm arrangement was a "big step closer".
Time is running out to reach a deal before 31 December, when the UK stops following EU trading rules.
Major disagreements remain on fishing rights, business competition rules and how a deal will be policed.
The dinner was seen as a last-ditch opportunity to work through the main sticking points and for the two sides to try and find some common ground.
Speaking before he left for Brussels, Boris Johnson said the EU was insisting on terms "no prime minister could accept" in relation to access to UK fishing waters and retaliatory measures if the UK diverged from EU standards.
Communities Secretary Robert Jenrick told ITV's Peston that there had been "no clear movement" and "very serious disagreements" had yet to be overcome.
Labour's Jonathan Reynolds told BBC's Newsnight the UK's approach was "not good enough" and ministers must deliver a deal "because that is what they promised and that is what people quite reasonably expect".
"No deal is clearly a nightmare scenario for most people in the UK," he said.
Brexit - The basics
- Brexit happened but rules didn't change at once: The UK left the European Union on 31 January 2020, but leaders needed time to negotiate a deal for life afterwards - they got 11 months.
- Talks are happening: The UK and the EU have until 31 December 2020 to agree a trade deal as well as other things, such as fishing rights.
- If there is no deal: Border checks and taxes will be introduced for goods travelling between the UK and the EU. But deal or no deal, we will still see changes.
Details of Northern Ireland agreement
In separate talks on Tuesday, the UK and EU reached an agreement on specific trade arrangements for Northern Ireland - including on post-Brexit border checks and trading rules for Northern Ireland.
From 1 January, Northern Ireland will stay in the EU single market for goods as the rest of the UK leaves.
That means a proportion of food products arriving in Northern Ireland from Great Britain will need to be checked under arrangements known as the Northern Ireland Protocol.
- All goods going from Britain to Northern Ireland will be exempt from EU tariffs, with a handful of exceptions
- NI supermarkets and suppliers won't have to carry out food safety checks on GB goods for three months
- There will be a longer six month "grace period" for checks on chilled meat products, such as sausages
- NI firms won't have to complete GB export declarations except in a very few cases
- Subsidies for NI fishing and farming businesses will be exempt from EU state aid rules
- EU customs officials will be able to observe border checks but not carry them out
Speaking in the Commons, Gove said it would ensure the smooth flow of trade "on which lives and livelihoods depend....with no need for new physical customs infrastructure" on the island of Ireland.
"The deal protects unfettered access for Northern Ireland businesses to their most important market," he said.
- BBC