“Is the troika learning from its mistakes?” asked Capital Economics, a British research group, in a research note released Friday. It said the I.M.F.’s admission that “mistakes were made” raised hope that the troika “might be becoming more realistic about the demands that they should make of struggling euro zone members.” But it added that the I.M.F. and its two partners differed on how far the softening of austerity should go, with the European Central Bank still championing the cause of “fiscal consolidation.”

Disbanding the much reviled troika, or at least overhauling its crisis management strategy, will not be easy. Addressing the European Parliament last month, Jörg Asmussen, Germany’s representative on the board of the European Central Bank, acknowledged that “the setup is a bit strange” and said it “has to be changed.”

But he added that as long as Europe’s economic crisis continued and countries remained under programs negotiated by the troika, the current state of affairs must remain in place. “We have no alternative to it right now,” he said.

Mr. Rehn, in an interview last month, acknowledged complaints in the European Parliament that the I.M.F., an outsider, did not have to answer to European institutions and that each of the three members of the troika had “its own philosophy and rules and a very strong sense of independence,” and putting them together was always going to be difficult. But, he added, “It has worked in practice even if it might not have been possible to work in theory.”

All the same, he said, change is still needed, particularly in relation to decision-making in the 17-nation euro zone. One big problem, he said, is that when finance ministers of countries using the euro meet to discuss a possible bailout, they must agree unanimously before anything can be done. “By definition the rule of unanimity makes decision-making much less effective and efficient than it should be,” he said.

The 50-page I.M.F. report released Wednesday did not provide a general survey of what had gone wrong in Europe, but focused on mistakes in Greece’s first bailout in 2010, which totaled about $143 billion. A major error, it said, was not to force investors holding Greek bonds to accept losses from the start — instead of waiting until late 2011 — so as to reduce the pressure on the government to cut spending. One reason this did not happen, according to the I.M.F., was opposition from the European Commission.

Though cast in part as a mea culpa by the I.M.F., the document has hit a raw nerve in Brussels, where officials have mostly refrained from criticizing the fund despite quarrels behind closed doors. There have been frequent tensions within the troika, with some European officials aghast at what they regarded as the I.M.F.’s insistence on unrealistic debt targets for Greece. Negotiations over what to do about Cyprus also created friction, particularly over a quickly aborted initial plan that involved seizing a portion of insured bank deposits held by savers with less than 100,000 euros in their accounts.