Donald Tusk has issued a "last call" to the UK to "lay the cards on the table" if a Brexit deal is to be done in time.
The European Council president said the "most difficult" issues were unresolved and "quick progress" was needed if agreement was to be reached by October.
Talks continue over the terms of the UK's withdrawal from the EU in March next year. What happens to the Irish border remains a sticking point.
The UK says both sides want to see a "faster pace" in talks.
But Prime Minister Theresa May has been unable to say much new at this summit - the last one before October - because she has yet to get her cabinet to agree on a blueprint for the UK's future relationship with the EU.
They are due to meet at Chequers next Friday, in what has been billed as a make-or-break meeting. Mrs May has said the UK will then publish a White Paper setting out "in more detail what strong partnership the United Kingdom wants to see with the European Union in the future".
Chancellor Angela Merkel said Mrs May would "come to Germany and we will have a longer debate on this", once the proposals were published.
At the close of the summit, Mr Tusk told reporters there was a "great deal of work ahead" on Brexit and the "most difficult tasks are still unresolved".
"Quick progress" was needed if a deal was to be reached at the next summit.
"This is the last call to lay the cards on the table," he said.
Waiting for Chequers
By the BBC's political editor Laura Kuenssberg
European leaders can repeat the same message, louder and louder.
But this EU summit's instructions to Theresa May may as well have been shouted into an empty cupboard.
Because they know what she knows - that the past 24 hours of Brexit conversations are not nearly as important as the next seven days of discussions at home between Number 10 and the rest of the government.
And after more than two years, this time next week ministers should be nearing the conclusion of their country retreat at Chequers.
It's there that the prime minister hopes to find resolution in her team on a more detailed offer to the rest of the EU - easing, if not removing, all the contradictions in the Tories' positions.
He was one of a string of EU chiefs demanding more clarity from the UK prime minister, who left the summit before the 27 other EU leaders discussed Brexit together on Friday.
European Commission President Jean-Claude Juncker said the British had to "make clear their position" adding: "We cannot go on to live with a split cabinet. They have to say what they want and we will respond to that."
EU chief Brexit negotiator Michel Barnier warned: "The time is very short" and that while progress had been made, "huge and serious divergence remains, in particular on Ireland and Northern Ireland".
He also said he hoped to see "workable and realistic" proposals from the UK on what the future relationship between the UK and EU should look like.
He said he was "ready to invite the UK delegation to come back to Brussels next Monday" to continue working on a deal.
BBC political editor Laura Kuenssberg said she understood that UK officials had already informed the EU Commission they would not hold talks on Monday and the "mini row over diaries" revealed "how tetchy things are".
Tensions revealed sometimes by tiny things - I hear Commission asked UK for talks next week, UK said no, so Barnier then invited them again in front of the cameras— Laura Kuenssberg (@bbclaurak) June 29, 2018
European leaders at the summit welcomed progress on the legal text of the withdrawal agreement but noted that "important aspects still need to be agreed" including the territorial application of the deal "notably as regards Gibraltar". Talks between Spain and the UK over Gibraltar, including access to its airport and the exchange of tax information, continue.
They also expressed concern that "no substantial progress has yet been achieved on agreeing a backstop solution for Ireland/Northern Ireland", if a deal on customs arrangements is not agreed by December 2020. when the transition period is due to end.
And they called on member states and EU institutions "to step up their work on preparedness at all levels and for all outcomes" - the European Commission president has said the EU must prepare for the possibility that no Brexit deal will be reached.
Mrs May's own cabinet is divided over what the UK's customs arrangements after December 2020 should look like, when the transition period agreed with the EU is due to end.
And there are disagreements over the future movement of goods and people across the border between Northern Ireland and the Republic of Ireland.
But asked if he believed Mrs May could resolve the differences, Mr Juncker told the BBC he knew the prime minister and: "yes ... she will".
Juncker tells us he believes the PM can get the cabinet to agree because ‘I know the British Prime Minister’— Laura Kuenssberg (@bbclaurak) June 29, 2018
On Thursday, Mrs May said a strong future partnership with the EU was in everyone's interests.
"I think both sides are keen to continue that work at a faster pace than we have done up till now and certainly we would welcome that," she said.
She added that the UK would publish a White Paper setting out "in more detail [the] strong partnership the United Kingdom wants to see with the European Union in the future".
But she urged fellow EU leaders to tell their negotiators the UK should be allowed to continue to take part in schemes like the Prum mechanism for sharing DNA profiles, the Second Generation Schengen Information System - a database of "real time" alerts about certain individuals - and the European Criminal Records Information System.
Without UK participation in such schemes, she suggested their collective ability to fight terrorism would be reduced.
Mrs May's Europe adviser Olly Robbins and Brexit Secretary David Davis were due to appear in front of the UK's Brexit select committee next week but it is understood that the appearance has been delayed until after the publication of the White Paper.
Former Brexit minister Lord Bridges, who backed Remain in the EU referendum, told the Evening Standard there was a risk negotiations could become a "rout", if the cabinet could not compromise, first with each other, then with Europe.
"If nothing changes, there's a danger the UK will have to agree to a withdrawal treaty full of meaningless waffle on our future relationship with the EU," warned Lord Bridges.
"With so little leverage in the next phase, the negotiations would become a rout. Worse, uncertainty will drag on, damaging our economy."