Late Wednesday, EU President Herman Van Rompuy of Belgium postponed it by more than two hours.
Herman Van Rompuy, president of the European Council, welcomed the result of the referendum.
European Union leaders Jose Manuel Barroso and Herman Van Rompuy were among those present.
Mr Van Rompuy and Mr Barroso then gave a joint acceptance speech, in two parts.
European President Herman Van Rompuy is due to meet Greek leader Antonis Samaras on Thursday.
Mr Van Rompuy's proposed banking union could sever the dangerous link between governments and banks.
This two-tier structure will become a regular event, under proposals by Mr Van Rompuy.
But a big role in the negotiations will be played by European Council President Herman Van Rompuy.
German Chancellor Angela Merkel said Mr Van Rompuy would bring consensus and political competence to the presidency.
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Earlier on in the debate, Mr Van Rompuy said the meeting was "at times difficult, but fruitful".
The prime minister met European Council President Herman van Rompuy on Thursday morning, before formal talks began.
Baroness Ashton and Mr Van Rompuy were chosen unanimously by the 27 EU leaders at a summit in Brussels.
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You'll have five out of 27 European Union members there, plus of course President Van Rompuy and President Barroso.
Mr Van Rompuy said the deal amounted to a cut of roughly 34bn euro in both commitments and payments.
Mr Van Rompuy said the world was experiencing an upheaval not seen since the end of the Cold War.
The aim, as the European Council President Herman Van Rompuy said, was "to make the euro an irreversible project".
The White House summit, the first with EU leaders since Mr Van Rompuy took office, came amid new recession fears.
Mr. Putin attended the dinner, along with European Commission President Jose Manuel Barroso and European Council President Herman Van Rompuy.
European politicians, including European Council President Herman Van Rompuy and European Commissioner Jose Manuel Barroso, have also cancelled their trips.
In the end, finance ministers were largely bystanders as others, including European Council President Herman Van Rompuy, negotiated the final deal.
The President of the EU, Herman van Rompuy, said "the EU stands ready to offer its assistance in any possible way".
It is being left to Herman Van Rompuy, president of the European Council, to find a compromise and avert a breakdown.
Mr Van Rompuy has indicated that he would like to see "an enhanced role for European institutions", such as the European Parliament.
President Van Rompuy agreed on the importance of steps to strengthen the resilience of the eurozone and growth in Europe and globally.
Herman Van Rompuy called the meeting after disagreement over the contribution of banks and other private investors to a second rescue package.
The President of the European Council Herman Van Rompuy has defended her.
The President of the European Council, Herman Van Rompuy, has suggested a budget that would be 75bn euros less than the Commission.
As long as globalisation was seen mainly as economic, Europeans felt as if everyone could win from it, argued Mr Van Rompuy.
Mr Van Rompuy is offering an alternative plan, a fast-track "fiscal compact" that does not need lengthy ratification by parliaments or national referendums.
Mr Van Rompuy paid tribute to the post-war leaders of France and Germany who had forged the EU by uniting their economic interests.
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