British Prime Minister Boris Johnson and the head of the EU's executive, Ursula von der Leyen, agreed in a phone call on Saturday (October 3) to step up Brexit talks to close "significant gaps" barring a new trade partnership.
The two sides have said this week's round of negotiations aimed at getting a new, post-Brexit trade agreement from 2021 made some progress but not yielded a breakthrough.
The EU says a deal must be sealed by the end of the month - or in the first days of November at the very latest - to leave enough time for ratification in the bloc by the end of the year.
Johnson and von der Leyen discussed the next steps in their call on Saturday.
"They agreed on the importance of finding an agreement, if at all possible, as a strong basis for a strategic EU-UK relationship in future," they said in a joint statement.
"Progress had been made in recent weeks but ... significant gaps remained, notably but not only in the areas of fisheries, the level playing field, and governance," it added.
The two leaders instructed their Brexit negotiators, Michel Barnier and David Frost, "to work intensively in order to try to bridge those gaps".
Johnson said earlier on Saturday the UK continued to push for a Canada-style deal with the EU, but was also ready to sever current close-knit trade ties and default to general World Trade Organization rules, which include quotas and tariffs.
"I think there's a good deal to be done," he said. "There's a big opportunity for both sides to do well."
More trade talks are due in London next week and in Brussels the following week before the 27 national EU leaders meet on Oct. 15-16 to assess progress. London has also said it wants clarity by Oct. 15 on whether a deal is possible or not.
An estimated trillion euros worth of annual trade would be at stake if they fail to get an agreement.
The EU says it will not implement any new deal if London undermines their earlier Brexit divorce treaty with its draft Internal Market Bill.
With time running out, controversy over the new domestic UK law backed by Johnson has cast fresh doubt on whether a deal was possible. German Chancellor Angela Merkel, however, said on October 3 she was still "optimistic".
The EU believes the British government is split between hawks like Johnson's aide Dominic Cummings, the architect of the 2016 "Leave" campaign, and those Brussels sees as more moderate like Frost on whether to push for a deal or leave without one.
British foreign minister Dominic Raab, seen as part of the former faction, said separately on Saturday that the EU no longer had the power to treat Britain poorly.
"Yes, we want a free trade deal with the EU, but any deal must be fair. The days of being held over a barrel by Brussels are long gone," Raab told the Conservative Party's annual conference.