May launched a diplomatic offensive on the sidelines of a summit in Sweden, strolling with French President Emmanuel Macron along the port in the city of Gothenburg as she tried to break the Brexit stalemate.
May also met EU chief Donald Tusk and the premiers of Ireland, Poland and Sweden in a bid to convince them that Britain would make enough progress to open up talks next month on future trade relations and a transition period.
The EU has demanded Britain make "sufficient progress" on the key issues of its divorce bill, citizens' rights and the Irish border if it wanted an agreement to move on to talks on a future trade deal and transition period.
European Commission President Jean-Claude Juncker warned that the "clock is ticking" to reach a deal in time.
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After her meeting with former Polish premier Tusk, May's Downing Street office said they "agreed that there is more work to be done and discussed how to take further steps forward together in advance of the European Council in December."
Macron's Elysee Palace said the "brief encounter" was held at Britain's request, and stressed that it was not intended to bypass the EU's chief negotiator, Michel Barnier.
Barnier warned last week that Britain had just two weeks to meet the bloc's conditions. Failure to reach a deal in December would push back a decision until February or March, leaving little time for trade talks before Britain leaves the bloc in March 2019.
The Irish issue has become particularly sensitive, with Irish Prime Minister Leo Varadkar threatening to block progress in December without a "written" guarantee that there will be no "hard border" with British-ruled Northern Ireland.
In a swipe at Britain, he added: "It's 18 months since the referendum, it's 10 years since people who wanted a referendum started agitating for one, sometimes it doesn't seem like they've thought all this through."
British media reports have suggested May could be ready to double the UK's 20 billion euro ($24 billion) offer on the exit bill in a bid to clear what has been the most difficult hurdles in talks so far. The EU says the bill is around 60 billion euros.
May's government is still pressing for a quick transition to future EU-British ties while shrugging off EU pressure on the divorce terms.
British Foreign Secretary Boris Johnson said in Dublin today that doing so would help solve the Irish issue, while Barnier's British negotiating counterpart David Davis called on the EU to compromise across the board.
Swedish Prime Minister Stefan Lofven, who also held talks with May, said it was "very difficult to say" whether a deal was possible in December and added that London "needs to clarify what they mean about the financial responsibility."
Leaders signed a so-called European Pillar of Social Rights at the summit today.
The EU is looking to reboot the union based on plans by France's new president Emmanuel Macron and by Juncker.
"This is absolutely crucial for EU's legitimacy," Lofven told reporters at the meeting, the bloc's first social summit since one in 1997 in Luxembourg.