"[But] there is no change in content", he said.
Because her chief whip Julian Smith presumably has advised her that if she were to adopt the additional year of what the Brexiters see as pure vassalage - without simultaneously scrapping the backstop and Chequers - there would be (in the words of one) "the mother of all explosions". Another source familiar with the talks said that she told European Union leaders that she was open to an extension of the transition "in a cautious way".
German Chancellor Angela Merkel said that she still believes it's possible to conclude a "good and sustainable" agreement with Britain before its departure - but stressed Germany also is preparing for the risk of a no-deal departure.
However, a fraught weekend in Brussels culminating in UK Brexit Secretary Dominic Raab walking away from the negotiating table means a deal won't be signed off until November - if there is a deal at all.
The Irish border issue has been the main sticking point in negotiations, proposed solutions include keeping Northern Ireland in the bloc's customs union and single market for goods, or having a customs arrangement for the entire United Kingdom with the EU to avoid that possibility.
Like May, European leaders continue to express confidence a deal can be struck - even as they are growing fearful of an unruly separation.
EU sources said there would be no compromise on a permanent backstop, despite British hopes of securing a temporary arrangement to avoid being tied into the EU customs union indefinitely.
Mr Tusk has warned that without new "concrete proposals" from the British to break the logjam over the Irish border backstop, further progress on a deal may be impossible.
Mrs May did not answer a question about whether she had brought the "creative" new proposal that summit chair Donald Tusk has asked for, instead sticking to a rehearsed line that a deal could be done and that it was in the EU's interest to reach one.
Ryanair boss Michael O'Leary has said a hard Brexit could ground planes for up to three weeks as the prime minister heads to Brussels for a crunch meeting with European Union leaders to break the impasses in the negotiations.
However, there is no official summit taking place in November between European leaders so any extraordinary meeting will likely have to be decided today or in the weeks to come - depending on whether or not there is any progress in negotiations. Brexit must be orderly for everyone and for all the issues including the island of Ireland.
"We will take this time, calmly and seriously, to find this global agreement in the next weeks", he said.
With the impasse likely to continue, diplomats are beginning to expect that a deal might not be complete until December or January, making it very tight to ratify any agreement in domestic parliaments across the European Union, including the House of Commons.
It was hoped that today's meeting would be a prelude to discussing a deal ready for finalisation in November.
"I don't think it will happen, I don't want it to happen, it would be a disaster if it did happen, it must not happen".
Dalia Grybauskaitė, the president of Lithuania, warned that the talks were being set back by the disunity in May's cabinet.
"She said we will keep under consideration the issue of the transition period but she did not say anything in favour or against the three-year period". "They do not know themselves what they really want".
In a speech in London on Tuesday evening, John Major, a former Conservative Prime Minister, said the Brexit vote was a "colossal misjudgment" and that Brexit-backers sold the country a fantasy and would not be forgiven.
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