European Council president Donald Tusk told Theresa May "the ball is now in your court" as the pair discussed the Brexit process 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 wanted the process to start "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.
The talks at No 10 come after the British Prime Minister faced accusations of vagueness and contradiction over the Government's position on remaining in the European single market.
Mrs May has insisted she will not reveal her negotiating hand "prematurely".
The meeting comes after she slapped down the UK's Brexit Secretary David Davis for suggesting that continued membership of the free trade zone was "very improbable".
Mr Davis's comment appeared to play into the hands of EU countries who have insisted that Britain cannot have full control over its borders and remain a member of the single market.
Mrs May told MPs on Wednesday that she was seeking "the right deal" on trade in goods and services after Britain withdraws from the EU, but added: "We will not take decisions until we are ready, we will not reveal our hand prematurely and we will not provide a running commentary on every twist and turn of the negotiations."
She refused to say whether she wanted the UK to remain in the European single market.
The British PM and her ministers were accused of "waffle" by Scottish National Party Westminster leader Angus Robertson, while the Liberal Democrats' Tim Farron said: "This Government isn't concealing its hand - it hasn't got a hand or, it would appear, a clue."
Jeremy Corbyn accused the British Government of issuing "contradictory messages" on Brexit which were exacerbating "huge uncertainty" about the UK's future.
But the Labour leader found himself in a row over the single market after a senior aide suggested he might rule out full membership unless Britain can negotiate exemptions from key EU rules.
That prompted Mr Corbyn's team to stress that he backed "full access" to the single market for goods and services but opposed certain directives linked to it, such as state aid rules and requirements to deregulate and privatise public services.
Following the 75-minute meeting, Mrs May's official spokeswoman played down suggestions that Mr Tusk's comments were intended to put pressure on the PM to hasten the invocation of Article 50.
"What the president said was that the ball is in our court, which it is," the spokeswoman told a regular Westminster media briefing.
"It's for the member state to decide."
She added: "There wasn't a sense in the meeting that we are under pressure on this, there was a sense that they accept 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.
"We want to take the time to prepare for the negotiations by talking to stakeholders up and down the country and doing the work here.
"The EU also needs to take time to prepare for the negotiations in terms of what approach the 27 will take."
The spokeswoman characterised the mood of the pair's first formal bilateral meeting, which took place over a breakfast of fresh fruit and scrambled eggs with smoked salmon, as "quite relaxed, friendly and warm".