The governments of France and Belgium agreed to nationalize Belgium’s largest bank on Sunday as the Greek debt crisis took its biggest victim yet, while France and Germany’s leaders promised far-reaching changes to the euro zone’s economic governance in a bid to stabilize Europe’s reeling finances.

Dexia, a Franco-Belgian bank that had a debt exposure totaling more than $700 billion at the end of June — more than twice the size of Greece’s annual economic output — had invested heavily in European government bonds whose value is now under question.

The nationalization is a sign of the spiraling problems facing European banks and governments, and it may threaten Belgium’s credit rating, making it one of the countries on shaky financial ground alongside Greece, Ireland, Italy, Portugal and Spain.

German Chancellor Angela Merkel and French President Nicolas Sarkozy said after a meeting in Berlin on Sunday that they are ready to recapitalize banks that have been shaken by the debt crisis. Merkel and Sarkozy are trying to head off a contagion that could balloon as large as the 2008 credit crunch that followed the default of Lehman Bros., this time with government borrowing as the culprit, not subprime housing loans. The leaders said they will announce more fundamental reforms to the euro area’s common economic governance by the end of the month.

“We are determined to do what’s necessary to secure the recapitalization of our banks,” Merkel said at a joint news conference with Sarkozy. Of the broader issue of coordinating economic policies for countries that share the same currency, she said, “We must consolidate the system. We must develop better foundations.” But she and the French leader declined to provide more specifics.

“Europe chose a single currency without considering what its economic governance might have been, without considering the harmonization of fiscal and economic policies,” Sarkozy said. “So now it’s up to us, in the midst of this crisis, to tackle those problems.”

Moody’s Investors Service on Friday placed Belgium’s Aa1 credit rating on review for a possible downgrade because of the expected costs involved in bailing out Dexia and guaranteeing that no investors’ deposits are lost. France and Belgium became part owners of the bank in 2008 after an $8 billion bailout, and the bank has made extensive loans to local governments in France.

On Monday, Dexia Bank announced that the Belgian government would buy its Belgian consumer banking division for $5.4 billion. Two French banks with government ties were negotiating to back the French division of Dexia that is a major lender to local governments. Dexia was negotiating the sale of its smaller Luxembourg division to a group of international investors and Luxembourg’s government.

The governments of Belgium, France and Luxembourg also agreed to provide funding guarantees of $121 billion for the next 10 years. Belgium will assume 60.5 percent of the burden, France 36.5 percent and Luxembourg 3 percent.

Belgian Prime Minister Yves Leterme and French Prime Minister Francois Fillon released a joint statement Sunday saying that a solution had been reached as “the result of intense consultations with all partners involved.” Trading on the bank’s stock was halted Thursday after it plunged more than 40 percent last week.

Belgium’s public debt, compared with the size of its economy, is the third-highest in the euro zone, after that of Greece and Italy. France is worried that its AAA credit rating may be jeopardized if it must spend large sums of money on recapitalizing its banks, which are significantly more exposed to Greek debt than banks in Germany. The International Monetary Fund has said that recapitalizing banks could cost $270 billion.

France has appeared to favor using the $569 billion euro bailout fund, known as the European Financial Stability Facility, to recapitalize banks, rather than risking exclusively its own money. Markets have been pricing Greek bonds at only 40 percent of their face value, reflecting the expectation that the country will not be able to fully repay them. European policymakers speak privately of making lenders to the Greek government write off half of their loans.

Merkel said last week that she would be in favor of a coordinated effort to recapitalize shaky banks but that she would want to use the bailout fund only as a last resort if banks were unable to raise money on the open market and their governments were unable to shore them up. Merkel and Sarkozy played down any differences Sunday, saying that they were in agreement about what was needed.

Surrendering any amount of sovereignty over economic issues has been a thorny topic for members of the European Union. But the financial turmoil in the euro area’s weaker countries — Greece, Ireland and Portugal have all needed bailouts — has dramatized the need to tackle the problem of 17 countries that are bound to one another by a common currency but that have economies that move at different speeds in different directions.