“We are determined to do everything necessary to ensure the recapitalization of Europe’s banks,” Chancellor Angela Merkel said in Berlin after meeting with President Nicolas Sarkozy of France.

But beyond promising closer coordination of economic policies for the euro zone, the two leaders declined to provide specifics on how the recapitalization would work, or how much money they would commit. The continued uncertainty could unnerve investors who hoped to see the governments take more decisive action.

The announcement came on the same day that the governments of France, Belgium and Luxembourg agreed to nationalize Dexia, Belgium’s biggest bank, infusing it with billions of euros in taxpayer money after it became the first casualty of the Greek sovereign debt crisis. Government officials had raced to prop up Dexia before global financial markets opened on Monday.

Dexia, which had received a bailout in 2008, “is the biggest euro zone bank failure in quite some time,” said Peter Zeihan, vice president of analysis at Stratfor, a geopolitical risk analysis company based in Austin, Tex. “It will force investors and shareholders to take second look at what they thought was stable.”

Banks like Dexia have become a flashpoint for European governments as they try to rein in the region’s debt woes without worsening their own finances. Mrs. Merkel, Mr. Sarkozy and others have only recently conceded that European banks may not be as sheltered from the storm as first thought, especially if the sovereign debt situation ensnares larger countries.

If that were to happen, other banks in Europe and the United States — as well as the governments themselves — could come under further pressure.

But Europe’s leaders remain at odds on how to achieve their goals, including the best way to shore up bank finances.

France, for example, wants to pump money from a developing bailout mechanism, the European Financial Stability Facility, into the banks, while Germany insists that the fund should be used only as a last resort, if the banks are not able to raise more money on their own.

The International Monetary Fund has estimated that Europe’s banks may need up to 300 billion euros, or about $400 billion, more capital if the debt crisis widens.

On Sunday, neither Mrs. Merkel nor Mr. Sarkozy put forth their own figure, saying they needed to consult with other European leaders. But Mrs. Merkel emphasized that European leaders would do “everything necessary” during a series of upcoming meetings, including one involving the 27 European Union leaders this week.

The bailout of Dexia comes as both governments are trying to pay down their own countries’ deficits and debts. In France, some officials have sounded the alarm that too big of a bailout for Dexia could menace the nation’s sterling debt rating, a notion the finance minister, Francois Baroin, has been quick to dismiss.

Belgium is in a more difficult situation. Its debt is 97.2 percent of gross domestic product, the third highest in the euro zone, after Greece and Italy. Moody’s Investors Service on Friday warned it could downgrade Belgium’s rating if support of Dexia lifted Belgium’s debt and investors started pushing up its borrowing costs. Officials say the bailout of 4 billion euros would not raise its debt much higher.

It was the second bailout in three years for Dexia, a lender to European and American cities that got into trouble in 2008 after a huge portfolio of subprime loans it owned went sour. Dexia received billions of euros from France and Belgium, and was the biggest European recipient of loans from the Federal Reserve’s discount window at the time.

Dexia, which has global credit exposure of about $700 billion, plans to create a so-called bad bank to house its troubled assets, including billions of euros’ worth of Greek, Italian, Portuguese and Irish debt. On Sunday night, the governments were still haggling over how to split the bill.

France gave Belgium approval to buy up to 100 percent of Dexia’s Belgian consumer bank, Bloomberg News reported. Dexia’s French municipal financing arm would be split from the group and merged with the French state bank Caisse des Dépôts and the banking arm of the French postal service, Banque Postale.

Dexia had almost recovered from its previous stumble when its troubles flared anew in recent weeks. Indeed, just three months ago, Dexia passed a round of stress tests for European banks, although regulators last week ordered a review of those tests to account for a lower value of government debt.

This month, banks rapidly started pulling back on lending to Dexia, and Moody’s placed the bank on review for a downgrade.

Last week, Dexia’s stock price plunged 42 percent and, as it neared collapse, trading in its shares was halted on Thursday.

Dexia’s fortunes, and those of many European banks, remain tethered to what happens to Greece. Germany’s finance minister, Wolfgang Schäuble, said in an interview with the Sunday edition of the Frankfurter Allgemeine Zeitung “that we assumed in July a level of debt reduction that was too low” for Greece, implying Greece faced difficulties ahead and even more support.

Mrs. Merkel, now increasingly concerned about any run on the banking system, told finance ministers and leaders from the World Bank and the I.M.F. last week in Berlin that Germany supported a coordinated bank recapitalization program.

Mrs. Merkel does not want to funnel more taxpayer money to the banks before they try going to the markets to raise capital. But she acknowledged in recent meetings in Berlin with World Bank and I.M.F. officials that Germany would not hold back in bolstering the banks if necessary. Failure to do so, she said, would lead to “vastly higher damage.”

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