BRUSSELS  - EU leaders threw British Prime Minister Theresa May a lifeline in Brexit talks, agreeing at a Brussels summit to start preparations for the next stage of negotiations.

EU President Donald Tusk said reports the talks were in deadlock were "exaggerated", hailing a speech May made in Florence last month for breaking the impasse. As expected, the other 27 leaders agreed there had been insufficient progress on the divorce talks to officially move on to the future relationship, delaying the decision to a December summit. But they took just 90 seconds to approve the start of internal preparations for post-Brexit trade and a transition deal, work that Tusk said would take Britain's proposals on future relations into account.

And a French presidency source said "scoping work has already broadly started", referring to preparations on the broad areas a deal might cover. "My impression is that reports of the deadlock between the European Union and the UK have been exaggerated, and while progress has not been sufficient, it does not mean there is no progress at all," Tusk said. May has struggled to contain divisions in her government since losing her parliamentary majority in a June election, and appealed to European leaders over dinner Thursday to help her make headway in the Brexit talks.

A European diplomatic source said: "May asked for a sign, we have given a sign." In a move that risks being seen as a snub to the EU's gesture, however, she repeated Friday that a detailed agreement on one of the biggest sticking points -- the financial settlement -- must wait. "The full and final settlement will come as part of the final agreement that we're getting in relation to the future partnership," May told reporters.

European capitals are demanding detailed written commitments on finance before consenting to the start of trade talks, fearing that Britain's departure in 2019 will blow a hole in the bloc's budget. Luxembourg Prime Minister Xavier Bettel warned: "We are not going to delay the bill indefinitely."

Like Tusk, German Chancellor Angela Merkel struck an optimistic note, saying after Thursday's dinner that she could see "zero indications that we will not succeed" in reaching a Brexit deal. However, French President Emmanuel Macron warned that agreement on a financial settlement was "a long way off".

"There is major work to be done on the United Kingdom's side," he said, adding: "Today we are not even halfway down the road."

 In Florence, May promised to maintain Britain's contributions for two years after Brexit to complete the current EU budget period, totalling around 20 billion euros ($24 billion).

European Parliament chief Antonio Tajani dubbed that sum "peanuts" this week and said it should be nearer 50 billion or 60 billion euros. May repeated Friday that Britain would also "honour the commitments" made during four decades of membership, and said officials were going through these "line by line".

The slow progress of the negotiations has stoked fears Britain could leave the EU in March 2019 without a deal in place, risking economic and legal chaos. Merkel, the bloc's most powerful leader, said: "I want very clearly a deal and not some unpredictable solution, on this we are working very intensively."

An EU source said that starting preparations on guidelines for the trade talks now would save time if and when the political decision was taken to move forward in December. As well as the financial settlement, the EU wants progress on the rights of three million European citizens living in Britain and the issue of the Irish border. May said the deal on citizens' rights was within "touching distance", and pressed her colleagues over a dinner on Thursday for "urgent" progress.

"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 told them. Dutch Prime Minister Mark Rutte said May "pleaded her case well", but called for more "concrete" positions in the run-up to December. A German government source said progress on citizens' rights had gone "very, very far" and crucial future EU-British ties "outweigh the current dispute about finances." The source concluded: "I believe everyone is aware of that and that is why we are optimistic that we are going to find a solution there -- with theatrical rumbling."