The Brussels summit has ended without agreement on the 27-strong union's next seven-year budget.
A BBC correspondent says another meeting will have to be called to sort out the difficulties but it is unclear how differences will be resolved.
European Council chief Herman Van Rompuy said he was confident a deal would be reached early next year.
Hours of talks failed to bridge big gaps between richer countries and those which rely most on EU funding.
The UK said current EU spending levels must be frozen.
The EU's divisions are very clear and have become even more stark at a time of economic crisis, says the BBC's Chris Morris in Brussels.
Mr Van Rompuy had reshuffled the allocations in his original proposed budget during the summit, but he kept in place a spending ceiling of 973bn euros (£783bn; $1.2tn).
With the eurozone's dominant states, Germany and France, unable to agree on the budget, UK Prime Minister David Cameron had warned against "unaffordable spending".
The failure to decide on a budget came just days after the finance ministers of the 17 eurozone states failed to agree on conditions for releasing a new tranche of bailout money to Greece, raising questions about the union's decision-making process.
Mr Van Rompuy's budget had been unacceptable to a number of other countries, not just Britain, Mr Cameron told reporters.
"Together, we had a very clear message: 'We are not going to be tough on budgets at home just to come here and sign up to big increases in European spending'," he said.
"We haven't got the deal we wanted but we've stopped what would have been an unacceptable deal," he added. "And in European terms I think that goes down as progress."
German Chancellor Angela Merkel said she was sympathetic towards Mr Cameron's view - but no more than she was to all countries involved in the discussion.
"The discussions, both the bilateral discussions and the common discussion, have shown us that there is sufficient potential for an agreement," she added.
French President Francois Hollande said the summit had made "progress".
"There were no threats, no ultimatums," he told reporters. "Angela Merkel and I both agreed that it would be better to take some time out because we want there to be an agreement."
Without naming the UK, he also said it was time the system of budget rebates was reconsidered.
"It is a paradox, because some net contributors [EU countries that pay in more than they get back] get some of the money back even though they are in a situation where they are wealthy enough for them not to get this money back," he said.
Lithuanian President Dalia Grybauskaite remarked that the atmosphere at the summit had been "surprisingly good because the divergence in opinions was so large that there was nothing to argue about".
European Commission chief Jose Manuel Barroso said the talks had failed owing to "important differences of opinion - especially in overall size of the budget".
The Commission, which drafts EU laws, had originally called for a budget of 1.025tn euros.
Its position was supported by the European Parliament and many countries which are net beneficiaries, including Poland, Hungary and Spain.
While most EU members supported some increase in the budget, several, mostly the big net contributors, argued it was unacceptable at a time of austerity.
Germany, the UK, France and Italy are the biggest net contributors to the budget, which amounts to about 1% of the EU's overall GDP.
Mr Van Rompuy's revised budget would have softened the blow to the two main areas of spending: development in the EU's poorer regions, and agriculture.
Instead, there would have been greater cuts to energy, transport, broadband and the EU's foreign service.
His proposal, put to leaders on Thursday evening, would have made no change to the level of administrative costs - something the UK might have found unacceptable.
Speaking after the summit, Mr Van Rompuy said: "My feeling is that we can go further... It has to be balanced and well prepared, not in the mood of improvisation, because we are touching upon jobs, we are touching upon sensitive issues."
Failure to agree on the budget by the end of next year would mean rolling over the 2013 budget into 2014 on a month-by-month basis, putting some long-term projects at risk.
Analysts say that could leave the UK in a worse position, because the 2013 budget is bigger than the preceding years of the 2007-2013 multi-year budget.