Talks on a post-Brexit trade pact between Britain and the EU are expected to continue today as "significant differences remain".
A senior UK government source said: "Teams have been negotiating throughout the day and expect to continue tomorrow. Talks remain difficult and significant differences remain.
"We continue to explore every route to a deal that is in line with the fundamental principles we brought into the negotiations."
A deadline of midnight on Sunday had been set by the European Parliament for both sides to reach agreement on a free trade deal beyond which the parliament said it will not be prepared to ratify any treaty on time for 1 January.
Earlier, the British government said that unless the EU makes a substantial move in the fisheries negotiations, then there will be no overall future relationship agreement in the coming days and the UK will end the transition period with a no-deal Brexit in 11 days' time.
A UK source said the EU was continuing to make demands that were incompatible with Britain's independence and that London could not accept a deal that "doesn't leave us in control of our own laws or waters".
The warning followed an offer by the EU's chief negotiator Michel Barnier that would see 25% of the value of fish caught by European boats in UK waters transferred to the British fleet.
While London says it should be closer to 60%, the 25% offer alone has faced strong push back from the eight coastal member states.
The Killybegs Fishermen's Organisation said Mr Barnier's proposal would spell the ruination of the Irish seafood sector.
This afternoon, Mr Barnier said the talks were at a crucial moment, but they were continuing to work hard alongside their British counterparts.
Both ????&???? must have the right to set their own laws & control their own waters. And we should both be able to act when our interests are at stake. (2/2)— Michel Barnier (@MichelBarnier) December 20, 2020
Downing Street said on Saturday that the EU was "struggling to get the flexibility needed from member states".
A Brussels source pointed out that the EU was the member states and that Mr Barnier was there to protect the interests of Europeans.
A Government source acknowledged the 11th-hour negotiations had taken a turn for the worse.
There is speculation that British Prime Minister Boris Johnson will not want to compromise on Brexit amid a furious backlash over the latest coronavirus restrictions in London and the south-east of England.
Scotland's Sturgeon calls for extension to Brexit transition period
Scottish First Minister Nicola Sturgeon called on Mr Johnson to seek an extension to the post-Brexit transition period with the EU because of the need to tackle a new coronavirus strain circulating in the UK.
"It's now imperative that (the) PM seeks an agreement to extend the Brexit transition period. The new Covid strain - and the various implications of it - means we face a profoundly serious situation, and it demands our 100% attention," she said on Twitter.
"It would be unconscionable to compound it with Brexit."
Earlier, EU Commissioner Mairead McGuinness said the situation regarding post-Brexit trade deal talks is serious now, and that there needs to be a broader understanding from the UK side of what they are getting, as opposed to what they must concede.
Speaking on RTÉ's This Week programme, she said sovereignty cannot be unilateral and that there has to be respect from the UK for the EU position in the talks.
The European Parliament needs the text of trade deal today in order to ratify a deal by 1 January, and while talks remain ongoing, no agreement has yet been reached on the issue of fisheries.
Ms McGuinness said it was "not accurate" to say that fisheries was the last issue blocking a trade deal, but was getting the most attention, adding that while progress has been made on other issues such as governance and level playing field, they were still not fully resolved.
Additional reporting: Reuters