The International Monetary Fund said Tuesday that the euro, a currency born a decade ago out of the post-World War II urge to knit Western European nations more closely together, was under “a shadow” and hinted it might not survive the current battle over government debt.

With European leaders struggling to agree how to divide the costs of another Greek rescue program, the IMF said there was “no consistent road map ahead, leaving both orderly and disorderly outcomes on the table. . . . The reaction by national authorities and economic agents has been one of retrenchment, threatening to turn back the clock on economic and financial integration, the very foundation” of the Economic and Monetary Union (EMU).

Nearly two years after a crisis that began with the disclosure of Greece’s inordinate levels of public debt, and with three euro-zone governments now under IMF programs, the comments in a report released Tuesday mark the agency’s most explicit statement that the 17-nation currency union may be in jeopardy.

European leaders are set to meet in Brussels on Thursday amid renewed doubt about their ability to craft a durable fix for the euro. The London-based Capital Economics consulting firm has dubbed the summit the euro zone’s “last chance saloon.”

Leaders have ruled out a breakup of the euro zone as unthinkable. Such a move would end ambitions for a European currency to challenge the dollar as a world reserve and, depending on which countries would leave the currency union, possibly force a major reordering of world finances.

But a breakup has nevertheless been a staple part of the discussion since Greece’s problems became acute in the fall of 2009. Some analysts see the outcome as inevitable in a region where economic performance is diverging: Either stronger economies such as Germany will leave to protect themselves from paying for a succession of bailouts, or weaker ones will want to regain control of their own currency and monetary policy.

The inability of leaders to agree on a course of action has hardened those views.

Those leaders approved hundreds of billions of dollars last year for a bailout fund, ensuring that Greece, Ireland and Portugal could keep paying their bills. But it was not considered adequate for the scale of Europe’s problems — weak banks, weaker public finances, tangled governance and lagging growth, problems that have as much to do with economic structure and culture as with the availability of cash.

A breakup would be costly. In a study presented to the IMF, ING chief economist Mark Cliffe estimated that Greece’s economic output might fall as much as 10 percent if it pulled out of the currency union. Output throughout the region would also fall sharply.

But the risk, with each week of unresolved crisis, seems more concrete. The IMF has cited the euro zone’s problems as perhaps the chief risk to the global economic recovery. And analysts at Capital Economics said “a very decisive response which could be applied not just to Greece but also to Spain and Italy” was essential. Otherwise, they said, the situation could become “irretrievable.”

The euro-zone project has its roots in Europe’s two 20th-century wars and the desire to create a more closely federated group of nations. Much of that has been accomplished, with open borders that allow members of the European Union to travel freely and a common market without tariffs and economic barriers. The euro was meant as a capstone that would unify the major European powers further.

But a decade into the experiment, progress has stalled. Capital and labor still do not move freely, as they ideally should, among jurisdictions that share money, as is the case among U.S. states.

More notably in the current crisis, the lack of central control over government budgets means that the tax and spending decisions in one nation can, through their effect on the currency, become the problems of all the others. Banks also have influence that extends across national borders, but their regulation and oversight remain under the control of each individual country.

The IMF said in its report Tuesday that Europe’s leaders have not delegated enough of their power over issues such as banking regulation and public budgets to euro-wide institutions. While some changes have been made, the system “preserves national control over fiscal, macroprudential and structural policies,” the report said. “Staff considers some delegation of policy power to the center necessary to ensure the integrity of EMU.”

“It will be unavoidable to subordinate some sovereignty to the common good,” Luc Everaert, the IMF’s division chief for the euro zone, said in a conference call. Without such steps, “one cannot have a currency union.”

The summit Thursday is meant to form agreement on a new emergency program for Greece that may add as much as $100 billion in loans from neighboring governments. Negotiations are underway, as well, for banks and other private investors to contribute more than $40 billion by agreeing to maintain existing bond investments in Greece rather than withdrawing the money when the bonds come due.

The session is being watched closely at a time when pressure is rising on the economies of Italy and Spain, which are also heavily indebted but are so large it would be difficult to mount the same sort of bailout for them that was engineered for Greece, Portugal and Ireland.

In its report, the IMF warned of the implications of not halting the crisis in the smaller countries. The spread of Europe’s financial problems to “core” countries such as France could have global implications, it said.

President Obama spoke with German Chancellor Angela Merkel on Tuesday morning about the challenges facing the euro zone. According to the White House, the two “agreed that dealing effectively with this crisis is important for sustaining the economic recovery in Europe, as well as for the global economy.”

Staff writer Zachary A. Goldfarb contributed to this report.