The two leaders said last evening after a meeting in Berlin that they are fully aware of their responsibilities for stability of the euro and they are determined to do "everything necessary" to increase the capital structure of the region's banks.
"Ensuring a reasonable supply of credits is a basic condition for a good economic development," Merkel said.
The two countries shared similar views on increasing the capital structure of banks and the two nations have reached an agreement on the question of recapitalisation, she told a joint news conference with Sarkozy.
In this regard, they said they want the same criteria to be applied to all financial institutions.
Details will be disclosed at the end of this month when they have worked out a comprehensive package of proposals, Merkel said.
Sarkozy said that a durable solution to the debt crisis must be found before the end of this month.
Europe must solve its problems before the G-20 summit, which he will be hosting in the French resort of Cannes early next month, he said.
The economy can prosper only when the banks are stable, Sarkozy said.
The two leaders also reaffirmed their support for heavily-indebted Greece to remain in the euro zone.
Merkel said Germany and France are in close contract with the "troika" of experts of the European Union, the European Central Bank and the International Monetary Fund (IMF) currently assessing Greece's implementation of the conditions agreed for the first financial bailout of 110 billion euros, which it received in May last year.
She expressed the hope that their report will provide some new ideas for a long-term solution to the Greek debt crisis.
Merkel and Sarkozy noted with satisfaction that the ratification of the euro zone nations' financial rescue fund, the European Financial Stability Facility (EFSF), will soon be completed and it can come into force.
In this respect, they will make proposals for closer cooperation among the EU nations in the areas of economic and financial policies, the leaders of the euro zone's biggest economies said.
Sarkozy said he agreed with Merkel on working for a "durable" and "global solution" to the euro zone debt crisis.
There will be more meetings, including the European Council and a meeting of the euro group of finance ministers, before the end of this month to finalise the details of their proposal.
Germany and France will take a common position on all issues at the forthcoming G-20 summit, he said.
As far as Greece is concerned, Germany and France want their partner to remain in the euro zone, Sarkozy said.
"We will find solutions which will ensure the financial stability of Europe and will solve Greece's problems on a long-term basis," he said.
