British Prime Minister Boris Johnson and European Commission President Ursula von der Leyen instructed their negotiators to resume trade talks on Sunday in a last ditch attempt to bridge significant differences.
The decision to revive the long-running talks after they stalled on Friday over three of the thorniest issues suggests both sides believe there is still some hope they can secure a deal governing almost $1 trillion of trade a year.
But it was not clear whether either camp was ready to shift its position enough to allow the breakthrough that has proved elusive since Britain left the EU on 31 January and entered a transition period that runs until the end of the year.
In a joint statement, the two leaders said that while there were serious differences, "we agreed that a further effort should be undertaken by our negotiating teams to assess whether they can be resolved".
"No agreement is feasible if these issues are not resolved," they said after speaking for more than an hour on Saturday. "We are therefore instructing our chief negotiators to reconvene tomorrow in Brussels. We will speak again on Monday evening."
After months of negotiations, there has barely been any movement on three areas of disagreement - fisheries, ensuring fair competition guarantees and ways to solve future disputes.
Sources from both sides said that French demands over fishing rights in British waters remained a key issue, and some in Johnson's Conservative Party suggested that EU officials had to convince French President Emmanuel Macron to back a deal.
Two EU officials said the talks would resume where they had left off. One described the suspension and then resumption of talks as theatrics. "Each side needs a bit of drama to be able to sell this."
Johnson, a figurehead for Britain's campaign to leave the EU, must be able to convince Brexit supporters that he has secured a clean break, reclaiming what he called during last year's election campaign the country's sovereignty.
Von der Leyen does not want to offer too much to London for fear of encouraging other member states to leave and must also deliver a deal that does not alienate any of the 27.
Irish Prime Minister Micheal Martin welcomed the decision to resume talks, saying on Twitter: "Every effort should be made to reach a deal."
If the two sides fail to reach a deal, the five-year Brexit divorce will end messily just as Britain and Europe grapple with the vast economic cost of the Covid-19 outbreak.
Both sides acknowledge that time is running out and UK and EU sources gave a pessimistic readout following the call between Johnson and von der Leyen on Saturday.
With less than four weeks to go before Britain completes its journey out of the bloc, both sides must also get agreement on any deal from their parliaments and the EU executive needs to get approval from all 27 member states.
If the talks continue beyond Sunday, they may be further soured when the British government presses ahead on Monday with legislation that breaks an earlier Brexit deal by reintroducing contentious clauses the upper house of parliament removed.
The British government is also introducing a new piece of legislation which is expected to contain more provisions that undermine parts of the exit deal.
The clauses, which the government says it needs as a safety net to ensure unfettered trade between its four nations, might not be needed if London and Brussels agree a trade deal.