Speaking as he arrived at No 10 for talks with the Prime Minister, Mr Tusk repeated his demand that the UK move to end the uncertainty for the rest of the EU.
He told Ms May: “This is the position shared by all 27 member states. To put it simply, the ball is now in your court.
“I’m aware that it is not easy but I still hope you will be ready to start the process as soon as possible.”
Mr Tusk also tweeted: “Our goal to establish closest possible EU-UK relations. Ball in UK court to start negotiations. In everybody’s best interest to start asap.”
The demand is for Mrs May to speed ahead with triggering Article 50, the formal process that starts the two-year withdrawal process.
It appeared to pave the way for a difficult meeting, because the Prime Minister has repeatedly insisted she will not take that step until sometime next year.
However, speaking later, the Prime Minister’s spokeswoman denied any suggestion that the UK had been told to “get on with it”.
She told Westminster journalists: “What the president turned up and said was that the ball is in our court, which it is – it’s for the member state to decide
“In terms of timing, he didn’t say anything different to the statement that they put out the week after the referendum
“There wasn’t a sense in the meeting that we were under pressure on this. There was a sense that they accepted the position the prime minister has set out and that that should provide useful time to prepare for the negotiations, precisely because we want to have a smooth departure.”
The spokeswoman said Mrs May recognised the “need to get on with it”, adding: “The British people have made their decision and it is important that we take that forward.”
The pair met for 75 minutes, during which time Mr Tusk was served neither a Continental breakfast, nor a ‘full English’, but enjoyed fresh fruit, scrambled eggs and smoked salmon.
They also discussed “increasing sentiments of anti-globalisation”, the need to maintain sanctions against Russia, recent attacks on Polish people in this country and ratifying the Paris climate change deal as soon as possible.
In contrast to Mr Tusk, some EU leaders, including Angela Merkel, had, in recent weeks, rowed back on their early insistence that Brexit start quickly, appearing to recognise that the UK’s new Government needed time to work out what it wanted.
The Council President said the details of Brexit would not be discussed at next week’s European Council, in Slovakia, because Article 50 has not yet been invoked.
But he said the leaders of the other 27 EU nations would “discuss the political consequences of Brexit” for Europe, at a meeting Mrs May will not attend.
Mr Tusk added: “I have no doubt that at the end of the day our common strategic goal is to establish the closest possible relations.”
The meeting was Ms May's first with a top EU official since becoming Prime Minister in July.
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