The talks had continued late into Thursday night.
A revised proposal from summit chairman Herman Van Rompuy keeps the spending ceiling in place but reallocates funds.
UK Prime Minister David Cameron told reporters in Brussels on Friday that “it isn’t a time for tinkering” with the EU’s 2014-2020 budget. “We need unaffordable spending cut,” he said.
Mr Cameron’s office said the German Chancellor, Angela Merkel, was sympathetic to the argument for further cuts when she met him on Friday.
Earlier, Mrs Merkel said she doubted an EU agreement could be reached at this meeting.
On Thursday the opening of the summit was delayed for three hours because of stark differences over the budget plans.
Most EU members support an increase in the budget but several countries, mostly the big net contributors, say it is unacceptable at a time of austerity.
The biggest net contributors (those who pay in more than they get back) are: Germany, the UK, France and Italy.
But EU Commission data shows that in terms of per capita contributions the UK is sixth, after the Netherlands, Denmark, Sweden, Germany and Finland.
‘A lot of detail’
The revised plan from European Council President Van Rompuy keeps a total spending ceiling of 973bn euros (£783bn; $1.2tn). But the cuts to cohesion spending – money for Europe’s poorer regions – and to the agriculture budget would not be as deep. The cuts to cohesion would be 11bn euros less and for agriculture 7.7bn euros less.
Other spending items would be cut further to compensate, but there is no change in the proposed levels of administration costs – something which the UK may find unacceptable.
A top aide to Mr Van Rompuy, Richard Corbett, said the adjustments “reflect the large majority view of what came out of the bilateral talks” on Thursday.
“What he put on the table was already a reduction compared with the existing budget,” covering 2007-2013, he told the BBC.
Richard Corbett, advisor to the EC president, insists a deal can be reached
He said a deal “could still be put together, but there is a lot of detail to be gone through”.
Earlier, Mrs Merkel said “I think we’re advancing a bit, but I doubt that we will reach a deal”.
She has previously said that another summit may be necessary early next year if no deal can be reached now.
French President Francois Hollande also cautioned that an agreement might not be possible.
But he added: “We should not consider that if we don’t get there tomorrow or the day after, all would be lost.”
The 90-minute session late on Thursday followed a gruelling day of face-to-face meetings between Mr Van Rompuy and each of the bloc’s leaders, followed by a flurry of backroom discussions.
The EU Commission, which drafts EU laws, has called for an increase of 4.8% on the 2007-2013 budget – a position supported by the European Parliament and many countries which are net beneficiaries, including Poland, Hungary and Spain.
The UK is the most vocal of EU member states seeking cuts in the budget to match austerity programmes at home.
“No, I’m not happy at all,” Mr Cameron said about Mr Van Rompuy’s offer.
A Downing Street statement said Mr Cameron had stressed the importance of the UK keeping its budget rebate, worth 3.5bn euros in 2011.
The statement called the rebate “fully justified”. The EU Commission and some EU governments want the rebate scrapped.
Mr Cameron has warned he may use his veto if other EU countries call for any rise in EU spending. The Netherlands and Sweden back his call for a freeze in spending, allowing for inflation.
Poland and its former-communist neighbours, which rely heavily on EU cash, want current spending maintained or raised.
Mr Hollande has also called for subsidies for farming and development programmes to be sustained for poorer nations. France has traditionally been a big beneficiary of EU farm support.
Failure to agree on the budget 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.
The UK government could then end up with an EU budget higher than what it says it will accept now.