The EU Commission and European Parliament had asked for a budget rise of 6.8% in 2013.
But most governments wanted to limit the rise to just 2.8%.
The failure of the talks will dent hopes of agreement on the 2014-2020 budget, which is up for discussion later this month, correspondents say.
Friday’s dispute was over an extra 9 billion euros ($12 billion) in “emergency funding” for 2012, to cover budgets for education, infrastructure and research projects.
But Germany, France and other governments questioned the funding, and eight hours of talks produced no agreement.
“Under these conditions, we felt that negotiations which hadn’t really begun by six o’clock in the evening couldn’t reasonably be expected to finish during the night,” said the parliament’s lead negotiator, Alain Lamassoure.
At the European parliament, UK Conservative MEPs clashed with Parliament President Martin Schulz, a German Social Democrat, over the extra 9 billion euros shortfall for 2012.
In 2012 the budget was 129.1 billion euros, a 1.9% increase on 2011.
Among the schemes facing a shortfall this year is the Erasmus student exchange programme.
It has allowed nearly three million young Europeans to study abroad since it was launched 25 years ago.
In an open letter to EU leaders on Friday more than 100 famous Europeans, including film directors and footballers, warned that “thousands could miss out on a potentially life-changing experience”.
Friday’s talks did produce a declaration of political will to provide 670 million euros to earthquake victims in Italy, but no agreement on how to finance it, the European Parliament said.
It said that if no agreement on the 2013 budget could be reached in the next 21 days, the European Commission would look to revise its budget proposal.
The UK’s Financial Secretary to the Treasury, Greg Clark, said the EU needed to practice “fiscal discipline”.
“The UK and a number of other countries were very clear from the outset that the Commission and the European Parliament should not be asking taxpayers for billions of extra euros when the spending in member states is being reduced,” he said.
The UK government, led by the Conservatives, has also objected to a proposed increase in the multi-year budget for 2014-2020, threatening a veto if necessary.
An EU summit aimed at reaching a deal on that budget will be held on 22-23 November.
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