Brussels has been far more calm coming out of the summit than on past occasions.
But several leaders said it was up to May to act.
"We have identified all potential scenarios from a technical point of view", French President Emmanuel Macron said as the summit wrapped up.
"Now the key element for a final deal is on the British side".
"We know how divided British politics is at the moment, not just the Government, and the Government party but also Parliament itself". "It's time to stand aside and let someone who can negotiate get on with it".
Dutch Prime Minister Mark Rutte, traditionally an ally of May's in the bloc, said "we have the instruments on the table and it should be doable".
"These issues are still pending, but in the talks I had this morning with Prime Minister Theresa May, we encouraged one another to reach an agreement on two out of the four memorandums, those dealing with tax issues, which are the most flexible ones".
Donald Tusk, president of the European Council, told Theresa May to come up with a "creative solution" when she addresses the 27 EU leaders before the dinner, even though she "appears to remain in an impossible political position" at home.
According to the Guardian, EU leaders are ready to pursue "all avenues" in order to help the PM find a deal that would not automatically be voted down by Parliament when brought back to MPs and avoid the United Kingdom crashing out of the EU.
European Union leaders agreed to keep talking but refused to confirm a special meeting in November to seal the agreement, pushing any possible deal back to a December summit.
Britain officially is to leave the bloc in March and to have agreed to an exit deal well before then, but London and Brussels previously had agreed there would be a transition period to conclude at the end of 2020, by which time both sides hope some kind of trade agreement also would have been concluded.
Earlier, Ireland's Europe minister said she was "absolutely clear" Mrs May was still committed to an open-ended backstop over the Irish border.
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She mentioned " Snow White " as an example, stating that she was anxious about some of the lessons it could teach her daughters. Rescue yourself, obviously", the actress said. 'I mean, the songs are great, but do not give your voice up for a man.
He warned that solving the Irish border issue was a "prerequisite" for a successful outcome of Brexit negotiations, and that failure to find a resolution would spell disaster for striking any deal.
Unlike the special protocol on Gibraltar, which will be annexed to the UK/EU Withdrawal Agreement, the memorandums are not an essential part of the Brexit deal. It's a good idea.
"I believe a deal is achievable and now is the time to make it happen", the prime minister told journalists at the EU Council meeting on Wednesday.
"I think where there is a will, there is a way", German Chancellor Angela Merkel is reported to have said, while it is thought the President of the EU Commission, Jean-Claude Juncker, told leaders May needs "help" to sell a deal back in Blighty.
Last week, Ireland's opposition leader Micheal Martin wrote to Mr Varadkar suggesting they commit to maintaining the government in the current form until a Brexit deal is ratified.
And it is certain to involve a demand from Brussels for a further year's contributions towards European Union budgets, which could cost the United Kingdom as much as £9 billion. Many of them suspect the British leader is pursuing a strategy of delay created to push negotiations to the brink, at which point Europe would yield and the hardcore Brexiteers in the British Parliament would be hard-pressed not to accept May's version of withdrawal, even if they despise it as a capitulation.
A spokesperson for the Alliance Party said: "We are disappointed by the prime minister's refusal to engage with the remain parties collectively".
At the end of the summit, Mrs May said good progress was being made on the UK's withdrawal agreement, but acknowledged that "a few, but considerable, outstanding issues" remained to be resolved.
Merkel said: "Where there's a will, there should be a way".
And Tusk added: "What I feel today is we are closer to final solutions and the deal". He acknowledged the feeling "may be a more emotional impression than a rational one".
May conceded: "There will be more hard moments as we enter the final stages of the talks, but I'm convinced we will secure a good deal".
At present the two sides are proposing that Britain remains inside the European Union single market and is still bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.