British and EU officials are locked in a fourth round of negotiations this week ahead of a European summit in October that will decide whether "sufficient progress" has been made on divorce talks.
But Tusk praised a key speech by May last week in which she pledged legal guarantees for EU citizens living in Britain and offered to continue paying into the EU budget during a transition period of two years after Britain leaves the EU in 2019.
Tusk said the tone was "constructive and more realistic", adding: "The philosophy of having the cake and eating it is finally coming at an end."
The latter was a reference to a phrase used by hardline Brexit supporters in Britain about what the government's approach to negotiations should be.
The EU has decided that current negotiations should aim to resolve the status of EU citizens living in Britain; the bill Britain will have to pay for the divorce; and the question of what should happen to the Ireland-Northern Ireland border after Brexit.
Only if European leaders decide there has been "sufficient progress" on these three issues would negotiators be allowed to broach the more complex issue of future trade ties between Britain and the EU.
As he met May at Downing Street earlier today, Tusk said he was "much more optimistic" after her speech but added: "Of course, we still have to do something maybe more substantive."
May said: "I think that by being creative in the ways that we approach these issues we can find solutions that work both for the remaining 27 but also for the UK.
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