Twenty-three of the 27 leaders agreed to pursue tighter integration with stricter budget rules for the single currency area, but Britain said it could not accept proposed amendments to the EU treaty after failing to secure concessions for itself.
After 10 hours of talks, all 17 members of the euro zone and six countries that aspire to join resolved to negotiate a new agreement alongside the EU treaty with a tougher deficit and debt regime to insulate the euro zone against the debt crisis.
Sarkozy said the sticking point had been Cameron's insistence on a protocol allowing London to opt out on proposed change on financial services.
European Central Bank President Mario Draghi called the decision a step forward for the stricter budget rules he has said are necessary if the 17-nation euro zone is to emerge stronger from two years of market turmoil.
"It's going to be the basis for a good fiscal compact and more discipline in economic policy in the euro area members," Draghi said as he left the summit. "We came to conclusions that will have to be fleshed out more in the coming days."
Markets were initially spooked by the split in Europe, and by the prospect of potentially lengthy and uncertain negotiations on a new treaty.
The euro, shares and commodities fell in Asia because of growing doubts about whether Europe can forge a convincing financial firewall to arrest contagion in bond markets.