May will also have separate meetings with key figures on the border question: Tusk, European Commission President Jean-Claude Juncker and Irish Prime Minister Leo Varadkar.
But hopes of a November deal were fading as he added: "We need much time, much more time and we continue to work in the next weeks".
The EU is demanding new "concrete proposals" from Theresa May on how to end the deadlock in Brexit talks, warning that a breakthrough may not be possible without further movement from the UK. The so-called backstop is created to prevent a hard border on the island of Ireland after Brexit.
The concession, delivered to European Union leaders at a dinner in Brussels last night, means that Britain may not fully leave the auspices of the European Union until nearly six years after the European Union referendum, while potentially putting billions of pounds more into European Union budgets.
Expectations were low before this week's summit in Brussels, once dubbed a "moment of truth" for Brexit, after a breakdown in talks between the lead negotiators at the weekend. But after urgent talks on the Irish border on Monday ended without producing the hoped-for breakthrough, the gathering looked more like a therapeutic bonding session than an occasion to celebrate.
Mrs May's meeting with European Union states today was supposed to give the green light for a special summit in November to finalise the terms of Britain's withdrawal.
"We will take this time, calmly and seriously, to find this global agreement in the next weeks", he said.
Lithuanian President Dalia Grybauskaite said that 2 ½ years after Britain's Brexit referendum, the country had still not explained clearly how it wants to leave the EU. "That is the problem".
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In the last few years, Allen has financially backed expeditions searching for the remains of both Japanese and American vessels . Soon after leaving Microsoft , Allen launched Vulcan, a holding company for his diverse business and philanthropic interests.
Tens of thousands of people are expected to march in London on Saturday in support of a People's Vote being held on Britain's final Brexit deal.
Instead, a summit to seal a Brexit deal will only be called if and when the EU's chief negotiator Michel Barnier deems that there has been "decisive progress". She told reporters that "most of the issues" in the withdrawal agreement have been resolved - apart from the Irish border.
This week's summit in Brussels was billed as a "moment of truth" for negotiations on Britain's exit from the bloc but it seems the truth is that the two sides just can not agree.
Mrs May had been asked to come up with new "concrete proposals" to unblock the impasse on the backstop issue but while she received a polite reception for her 30-minute presentation to fellow European Union leaders, it appeared to have left them cold.
Does not want to see a gap between transition period and future deal.
An EU Commission source told Business Insider on Monday that they were more pessimistic than ever about the prospect of the United Kingdom being able to agree a deal before Brexit.
In a speech to the German parliament before travelling to Brussels, Chancellor Angela Merkel said that the possibility of a Brexit deal was "still there", but added that Berlin was making plans for a no-deal withdrawal.
The call from European Council president Donald Tusk came as Mrs May urged her Cabinet to "stand together and stand firm" on Brexit, after negotiations stalled in the run-up to a crucial summit.
There, EU leaders raised the possibility that the post-Brexit transition period, during which Britain would retain EU rules, could be extended by a year as a way to give London more time to agree the EU-UK customs deal it wants to solve the issue of the Irish border.