Theresa May has urged EU leaders to help her get a Brexit deal she can sell to the British public.
At a dinner with the leaders of the remaining EU states in Brussels, the prime minister said there was a "clear and urgent imperative" to give new impetus to stalled negotiations in order to achieve an acceptable outcome.
On the second day of the European Council summit on Friday, the remaining 27 will declare that insufficient progress has been made in withdrawal negotiations for trade talks to begin.
But German chancellor Angela Merkel gave Mrs May a boost by indicating there were "encouraging" signs that the EU might be able to "take the work forward and then reach the start of the second phase in December", adding that progress is being made.
However, Mrs Merkel also told reporters that while Mrs May is making more of an effort with EU partners, it is still "not enough".
Failure to secure the go-ahead for trade talks this month has fuelled pressure on Mrs May to begin expensive preparations for a "no-deal" Brexit, while a group of hardline Brexiteers - including four Tory former cabinet ministers led by ex-chancellor Lord Lawson - signed a joint letter urging her to walk away from talks.
Addressing her fellow leaders over dinner on Thursday evening, Mrs May said: "There is increasingly a sense that we must work together to get to an outcome we can stand behind and defend to our people."
Calling for "joint effort and endeavour" to inject momentum into the talks process, she told them: "The clear and urgent imperative must be that the dynamic you create enables us to move forward together."
Mrs May acknowledged that formal negotiations between Brexit Secretary David Davis and chief EU negotiator Michel Barnier had run into "difficulties" over the summer, and said that the UK was now determined to take a creative and pragmatic approach to moving the process forward.
While some leaders echoed Mrs Merkel's positive comments, some indicated they believe the onus is on Mrs May to make further concessions on the divorce bill, which Brussels sources have put at around £53 billion. Mrs May is believed to have offered just £18 billion so far.