European Council president Donald Tusk told Theresa May "the ball is now in your court" during Brexit discussions at Downing Street.
In a sign that Brussels was waiting for Mrs May to clarify when she will trigger Article 50, Mr Tusk said it was a "crucial time" for the UK and for the EU and he hopes the separation process will begin "as soon as possible".
The leaders of the other 27 EU nations will hold talks in Bratislava next week and Mr Tusk said they would "discuss the political consequences of Brexit" for Europe.
But he told Mrs May: "It doesn't mean that we are going to discuss our future relations with the UK in Bratislava, because for this - and especially for the start of the negotiations - we need the formal notification, I mean triggering Article 50.
"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.
"I have no doubt that at the end of the day our common strategic goal is to establish the closest possible relations."
Mrs May said she wanted a "smooth" Brexit process and told Mr Tusk they had "serious issues" to discuss.