Both nations are believed to have been reluctant to commit their taxpayers' money to a Europe-managed fund and instead advocate a case-by-case approach to rescuing financial institutions.
With the rescue fund seemingly ruled out, France, Germany, Britain and Italy were likely to focus on the need to work together after Ireland guaranteed deposits at its six major banks.
On Friday, Nicolas Sarkozy, the French president, wrote to Jose Manuel Barroso, head of the European Commission, stressing the need for an "intense effort of co-ordination and convergence" between EU states.
"Our citizens expect resolute action on our part to protect them," he said.
The Irish action drew criticism from Britain and other EU nations, who raised fears of capital flight from their banks to the better-protected Irish accounts.
The Irish government said it had no choice but to act in order to restore a sufficient level of confidence to improve their access to funds in capital markets.
Jean-Pierre Jouyet, France's minister for European affairs, said that EU nations needed to agree on "intervening where and when it is necessary to prevent any systemic risk. All European banks are related."
|Sarkozy met IMF chief Dominique Strauss-Kahn before the summit [EPA]
He told Les Echos
financial newspaper that European governments must look at co-operation on bank liquidity, credit lines and the system of asset-backed securities.
European governments have already had to step in and bail out several major banks, including Britain's Bradford & Bingley, Belgian-Dutch Fortis and Belgium's Dexia.
The summit came as the host nation became the latest country to fall into recession, according to official statistics.
The French economy shrank by 0.3 per cent in the second quarter of the year and on Friday the statistics agency forecast that gross domestic product would drop by a further 0.1 per cent in both remaining quarters of 2008.
Economists define a recession as two successive quarters of negative growth.
Max Keiser, a financial expert, told Al Jazeera: "This is a global war between savers and speculators.
"Henry Paulson, the US treasury secretary, who is a chief speculator, now wants to peddle hundreds of billions of dollars worth of US treasury bonds to Europe.
"I think the German leaders and the German people don't want them stinking up their banking system because they've already caused massive global banking failures."
The EU leaders hope to forge a common position on tackling the financial turmoil before heading to a Group of Eight meeting of finance ministers in Washington next week.
But Marc Touati, chief economist at Paris brokerage Global Equities, was pessimitic about whether anything tangible would be achieved.
"There won't be any big measures taken, unfortunately. The best we can hope for is some grand statement on maintaining European unity.''
Keiser also said: "Hopefully German mentality will prevail and we won't see the EU going down the path of hyper-inflation.
"You can't fight debt by issuing more debt. There needs to be a recognition of the basic underlying business model of speculation, over production, over workers is false. It didn't work. It's a 20-year neo-liberal model that has failed.
"They have to allow some of these banks to go bankrupt. The solution they are proposing is making the situation much worse."
As well as the four leaders and Barroso, Jean-Claude Trichet, the European Central Bank president, and Jean-Claude Juncker, the Luxembourg prime minister who also chairs the group of euro-zone finance ministers, will attend the meeting.