FRANKFURT — With an agreement to bail out Spain's struggling banks, Europe again avoided financial chaos in a debt crisis that is in its third year. But Europe still faces far bigger challenges that threaten the Continent and, with it, the world economy.
The most urgent of those concerns is being driven by events in a country at the other edge of the euro zone: Greece.
While the Spanish banking rescue will be expensive — as much as $125 billion — it will be well within the means of a European emergency fund established for just such purposes.
Far harder to calculate are the costs if, after Greek elections next Sunday, the new government reneges on the bailout Greece negotiated with its European lenders a few months ago. That could lead to a withdrawal from the euro zone, threatening that currency union, which has largely benefited more prosperous members like Germany.
What is more, the Spanish bailout will do little to address European banks' addiction to the borrowed money they have depended on for their daily financing needs.
"The way the currency union has been functioning is not sustainable," Jens Weidmann, the president of the German Bundesbank, told the Welt am Sonntag newspaper. "A breakup of the currency union would bring extremely high costs and risks that no one can really predict."
Lucas Papademos, a former interim prime minister of Greece, said that Greece's departure from the euro zone would be catastrophic, pushing inflation in the country to as high as 50 percent, putting extreme stress on Greek banks and slashing living standards.
"The stakes are exceptionally high," Mr. Papademos, who is also a former vice president of the European Central Bank, told a group of bankers in Copenhagen last week. "Because the decisions to be made at, and immediately after, the forthcoming elections will determine the country's future for at least the next decade."
Those problems would not be Greece's alone. Europe's big fear is contagion — an infection of financial panic that could spread far beyond Greece. Spain's leaders have long said Greece's problems contributed to the general market uncertainties that helped undermine Spanish banks.
On Sunday, Prime Minister Mariano Rajoy cautioned that the ailing Spanish economy, Europe's fourth largest, which has had an unemployment rate of nearly 25 percent, would worsen before getting better.
"This year is going to be a bad one," he said.
And it may not end there, with Italy struggling with economic stagnation and escalating borrowing costs.
A critical question will be how Saturday's deal will be received by investors on Monday, particularly with the Greek elections approaching.
"By no means is this a solution," said Adam Parker, chief United States equity strategist at Morgan Stanley. The aid for Spain "could be a near-term positive from a trading standpoint, but you haven't solved anything in the long term."
The next task for European leaders is to show the rest of the world that they are making a credible effort to repair the flaws in the euro zone that allowed the problems in one small country, Greece, to threaten the world economy.
On June 28 and 29, European Union leaders will gather in Brussels to discuss, among other things, ways to forge closer fiscal integration. Despite calls from some leaders for shared oversight of budgets and deficit spending, no concrete proposals have been made.
Even if Greece ends up with a government willing to try to live up to the terms of its 130 billion-euro bailout deal by meeting its payments and striving to narrow its wide budget gap, strong doubts remain whether any new leadership in Athens can fulfill those obligations. A lot of private money has already fled Greece, while its deeply depressed economy and dwindling tax revenues threaten to put the country even deeper in the hole.
"Even in case of a new government, I doubt whether the institutional framework in Greece can guarantee the program," said Jürgen Stark, a former member of the European Central Bank's executive board. "Who has the competence to implement the program? That is the key point."
Mr. Stark is among those who contend the euro zone is strong enough to withstand a Greek departure. "There will be contagion," he said in a telephone interview. "But I think it can be managed. It will be costly in the short term. There will be benefits in the long term."
Jitters about what Greek voters might do may have helped soften statements from Germany, the euro zone's paymaster, in recent days. Although Berlin has been Greece's harshest economic critic, Germans awoke last Thursday to find Angela Merkel, their chancellor, telling them on television that Europe needed a fiscal union — implying that some of their tax dollars may be needed to help the suffering Spaniards and Greeks.
"We need more Europe," Ms. Merkel said on ARD television. "We do not only need a monetary union, but we also need a so-called fiscal union. This means that we also need a common budgetary policy, and we also need a political union."
Such a statement might have provoked an outcry a year ago — Ms. Merkel quickly played down the prospect of a "big bang" solution coming from the gathering in Brussels — but Germans may be realizing that their own well-being is in imminent danger.
This week official data will provide more clues about how the crisis is affecting Europe's largest countries. Figures on industrial production in France and Italy are expected Monday and for the euro zone as a whole Wednesday.
Analysts have predicted declines, which would be bad for Germany because Europe's biggest trading partners are other European countries. But slower growth in Germany could also create a political backlash, making Germans more reluctant to help their stricken fellow euro zone citizens.
"If people think they are poorer maybe they become more reluctant to share the burden," said Clemens Fuest, economics professor at Oxford University.
Mr. Fuest said he was skeptical that Europeans would ever agree to delegate control over their national budgets to a European authority as part of a fiscal union. European leaders would be better off concentrating on measures that are more realistic, he said, like a common system for overseeing banks, guaranteeing deposits and dealing with sick financial institutions.
That could help avoid situations like those in Ireland, Cyprus or now Spain, where the cost of bank rescues raises doubts about the solvency of the national government.
Many proposals to push members of the European Union closer together would take years to carry out, too late to help ease current tensions. Mario Draghi, the president of the European Central Bank, said last week that it would help a lot if European leaders simply wrote a detailed plan for the future of the euro zone.
"The very fact of having an objective, a goal, an end point and a clear path would, by itself, contribute to a stabilization of the financial situation in Europe," Mr. Draghi said at a news conference.
How much time he and other leaders have to chart such a path may depend on what Greek voters decide.
"The Greek government, when one is formed, must send a clear signal that it is prepared to implement the reforms that have been agreed to," Mr. Weidmann, the Bundesbank president, told ARD on Sunday. "It's in the hands of the Greeks."
Nelson D. Schwartz contributed reporting from New York, and Raphael Minder from Madrid.