EU negotiator Michel Barnier vowed Tuesday to continue to push for a post-Brexit trade deal in the last 10 days before Britain leaves the single market.
"We are really in the crucial moment, and we are giving it the final push," Barnier told reporters as he headed into a meeting with EU ambassadors in Brussels
"In 10 days the UK will leave the single market and I will continue to work, in total transparency with the European Parliament and the member states," he said.
If the talks between Barnier and his UK counterpart David Frost fail to reach a breakthrough in the coming days, the UK will leave without a follow-on trade deal.
Tariffs would be reimposed on cross-Channel trade in food and goods, exacerbating the economic shock of a return to a border after 47 years of integration.
But the talks are deadlocked over how to ensure fair trade rules are respected in the future and, especially, over how to assign fishing rights in UK waters.
On Monday, British Prime Minister Boris Johnson and EU chief Ursula von der Leyen held a crisis call to discuss Brexit and the coronavirus crisis.
The call, revealed Tuesday by an EU source, came amid reports that Britain had improved its offer on fish, moving closer to Brussels' demand for long-term access.
But French officials told AFP that the British position had not yet moved far enough.
The two sides are haggling over the cut EU fishermen will take to their catch in British waters and the length of a transition period to phase in the changes.
- Travel ban -
The eleventh-hour talks have also been overshadowed by the fast-moving crisis over the new coronavirus strain found by London.
Amid reports the new mutation of Covid-19 might spread more quickly than previous ones, 40 countries in Europe and around the world cut travel links to Britain.
The EU is scrambling to come up with a coordinated response after cross-channel traffic was left snarled as France shut down entry for passengers and goods.
Ambassadors from the bloc's 27 members are to meet later Tuesday to try to hammer out a joint plan to allow cargo to start moving again and EU nationals to return home.
Von der Leyen's Commission has recommended that blanket bans be discontinued in order to allow essential passenger travel and freight shipments to resume.
But Germany and Ireland have already renewed their precautionary bans and France is in talks with London over instituting virus tests for truck drivers.