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May met the European Union's chief executive for about 90 minutes on Wednesday to try to hammer out a blueprint for Britain's ties after it leaves the bloc and to get commitments that will appease rebels at home opposed to her Brexit draft treaty.
"Very good progress was made in the meeting between President Juncker and Prime Minister Theresa May. Work is continuing," a Commission spokesman said after the meeting ended, declining to give more details.
May said she would be returning to Brussels on Saturday for more talks.
"There were some remaining issues which we have discussed," May said afterwards. "I will be returning on Saturday for further meetings, including again with President Juncker to discuss how we can ensure that we can conclude this process."
With just over four months before Britain's departure, May is trying to finalise an outline of future relations before a summit of EU leaders on Sunday to endorse the Brexit accord.
Raising the stakes, EU diplomats said they had been told that German Chancellor Angela Merkel was not willing to come on Sunday for any negotiations, meaning a text must be ready beforehand.
May and Juncker shook hands briefly in front of TV cameras at the Commission's headquarters before they went into talks but did not answer questions.
"The only thing really outstanding is Gibraltar," said one EU diplomat.
Spanish Prime Minister Pedro Sanchez has demanded assurances that the future of Gibraltar would be settled through direct talks with Madrid and said he would vote against the draft Brexit deal he didn't get them.
"If this is not solved by Sunday, Spain, a pro-European government, will unfortunately have to vote 'no'," Sanchez said at a joint news conference with his Portuguese counterpart on Wednesday.
Many in Brussels thought Sanchez was trying to score points with voters at home before a December 2 local election in the southern Andalusia region. They said the issue could be solved by the leaders and warned Madrid not to put the whole Brexit agreement at risk.
The British and European parliaments must ratify the tentative deal to end more than 40 years of partnership before Brexit day, or Britain could leave the EU with no treaty.
The publication last week of a draft exit treaty sparked the biggest crisis of May's premiership, with two cabinet ministers quitting and dozens of Conservative members of parliament calling on her to step down. They accuse May of making too many concessions to the EU, while others oppose Brexit altogether.
May hopes the blueprint on future relations - a political document of about 20 pages meant to be agreed side-by-side with the legally binding 600-page exit treaty - will help win back enough support at home for her approach to pass in parliament.
The Northern Ireland party whose 10 members of parliament back May's government does not plan to withdraw its support yet despite opposition to her withdrawal deal, its leader said on Wednesday.
"The confidence and supply agreement ... is very much still in existence," Democratic Unionist Party leader Arlene Foster told BBC television in an interview. "It is not dying."
Asked when the party might consider pulling the plug on support for May, Foster said: "Well we're not there yet."
But despite the political turmoil around her, May has shown no sign in public of any doubt that she can bring home a deal.
The draft treaty envisages Britain staying in a customs union with the bloc, which many Brexit supporters see as a compromise too far.
The EU is trying to discourage Britain from any renegotiation of the draft treaty, while also seeking to assuage concerns expressed by some of the remaining 27 member states. While unanimity among the 27 is not legally required to endorse the deal now, the bloc seeks a unified stance.
"We are following the latest developments with growing concern," said a second EU diplomat. "No one wants to reopen the withdrawal agreement."
Both sides have also been advancing contingency plans for the worst case scenario - Britain crashing out of the EU without an agreement.
Diplomats in Brussels said Britain was also seeking an easy flow of goods after Brexit, a position which was too close to the privileges allowed only for countries that sign up to EU single market rules, including free flow of people and services.
"The UK wants free movement of goods, which they won't get because that's back to discussing partial access to the single market, which we don't do," another diplomat said.
In addition, France has called for more guarantees on future access to Britain's fishing waters, which London wants to keep firmly under its control after Brexit.
EU envoys will meet on Thursday morning to discuss the outline of future ties. Negotiators will then look at it again at a meeting set for Friday before the Sunday summit.
Most in the EU are determined to get the deal over the line despite outstanding issues, with one diplomat saying: "There is plenty of negotiating time left to achieve that."