Sarkozy said that he and Merkel were confident the eurozone crisis would be solved "before the month is over," reports Business Insider.
However, the two leaders still need to settle their disagreement over how to use the $590 billion available from the European Financial Stability Facility (EFSF).
Merkel has argued that eurozone banks should turn first to their own investors to raise more capital. The French want to use the EFSF funds to recapitalize banks across the eurozone.
Merkel and Sarkozy also alluded to greater fiscal consolidation in the eurozone, suggesting that treaty revisions could be a next step towards a more stable eurozone, reports Business Insider.
Some of Germany's banks are already preparing to raise billions in new funds from private sources, the U.K. Daily Mail reports, an option said to be favoured by German Chancellor Angela Merkel.
Furthermore, adding to the urgency of the moment, the president of the European Union said Monday he is delaying next week's summit of EU leaders until Oct. 23 because they need more time to finalize a plan to fight a worsening debt crisis. The EU summit was originally planned for next Monday and Tuesday.
The new timing will allow the bloc "to finalize our comprehensive strategy on the euro area sovereign debt crisis," Herman Van Rompuy said in a statement.
Leaders need more time to conclude discussions on financial aid to Greece, the recapitalization of banks and giving the eurozone bailout fund more firepower, Van Rompuy said.
The 27-country EU, and in particular the 17-country eurozone, have found themselves under growing market pressure, as fears intensified that Greece and other highly indebted countries will default on their debts and take down big banks that hold their bonds.
Van Rompuy said he had also asked for an additional meeting of EU finance ministers ahead of the summit, so they can lay the groundwork for the leaders' decision.
With the time bought by delaying the summit, perhaps both the French and German leaders can reach a consensus on how to deal with the question of raising capital.
The Associated Press contributed to this story.