EU President Donald Tusk said in a tweet the bloc's other 27 leaders meeting in Brussels had agreed to begin preparations for trade talks even though not enough progress has been made on the terms of the divorce.
The news came after German Chancellor Angela Merkel struck an optimistic note following a summit dinner last night, saying that despite delays in the negotiations, she could see "zero indications that we will not succeed" in reaching a final agreement.
Written conclusions approved by the leaders said the EU will delay the decision on opening the next phase of talks until the next summit in December, but they will agree to "start internal preparatory discussions" on trade and a possible transition deal.
The slow progress of the negotiations, particularly on Britain's financial settlement, stoked fears it could leave the EU in March 2019 without a deal in place, risking economic and legal chaos.
Merkel, the bloc's most powerful leader, emphasised she did not want this, saying: "I want very clearly a deal and not some unpredictable solution, on this we are working very intensively."
May joined her 27 counterparts for a working breakfast on the future of the EU, before leaving them to discuss the state of Brexit negotiations.
The EU agrees that of the three key separation issues at stake, citizens' rights is the most advanced, but sticking points remain on the bill and Northern Ireland's border with Ireland.
European Commission chief Jean-Claude Juncker, who previously said it would take a miracle to move the talks on at this week's summit, today said: "I don't think there will be a miracle."
An EU source said that starting preparations on guidelines for the trade talks would save time if and when the political decision was taken to move forward in December.
A French presidency source added that "scoping work has already broadly started", referring to preparations on possible details of a deal.
May pressed her colleagues over a dinner of pheasant late yesterday for "urgent" progress on a deal she could sell to voters and her own Conservative party, which is still divided over Brexit.
"There is increasingly a sense that we must work together to get to an outcome we can stand behind and defend to our people," she said, according to Downing Street.
Dutch Prime Minister Mark Rutte said May "pleaded her case well", but she did not offer any more detail than in a speech she made in Florence in September.
He called for more "concrete" positions in the run-up to December.
European leaders have been increasingly vocal about their frustration at divisions in May's cabinet over Brexit, saying they are still unsure what Britain wants despite five rounds of negotiations.
The exit bill is the most poisonous issue, with Germany and France insisting that there should be no impact on the EU's budget from Britain's departure.
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