The failure to reach an agreement for the second week in a row highlighted the depth of differences among officials on how to find the money to keep the Greek economy afloat to contain contagion in the euro zone even as the country’s debt prospects worsen.
The German Finance Minister Wolfgang Schäuble told reporters after nearly 12 hours of talks that some of “the questions are so complicated we didn’t find a conclusive solution” and he said finance ministers would meet again on Monday to resume the discussions.
Mr. Schäuble also noted that European leaders could take up the discussions during a two-day summit here that begins Thursday.
While there is little immediate threat that creditors will deny further aid to the government in Athens, finding a formula to turn the spigot back on has proved intensely difficult, particularly for Germany, where Chancellor Angela Merkel is seeking to avoid making new financing commitments to the most vulnerable euro area countries like Greece ahead of her re-election campaign next year.
That has left the leadership of the euro zone jawboning at a seemingly endless series of late-night meetings.
Greece is seeking to unlock a 31.5 billion euros, or $40.2 billion, installment of loans from an international bailout program. If ministers do reach a deal, Greece is likely to get a larger amount of about 44 billion euros ($56 billion) because two additional installments are due by the end of the year under the program.
The current program, worth 130 billion euros (167 billion), has been frozen since June, when creditors determined that Greece was failing to meet the conditions of the bailout.
During the closed-door discussions that began on Tuesday evening, ministers and international officials also were at loggerheads over whether to give Greece two more years, to 2016, to reach a primary budget surplus, a concession requiring nearly 33 billion euros ($42 billion) on top of existing bailouts.
Christine Lagarde, the managing director of the International Monetary Fund, insisted that financing Greece to 2016 would help it to the path of making its debt manageable by the end of the decade.
But a number of member states resisted that suggestion, insisting on limiting questions of how to finance Greece thru 2014. Using a target date of 2014 would cost less, or about 15 billion euros, ($19 billion) but that would leave questions unresolved about the country’s financing.
In an effort to address the added costs, the ministers ranged over options from lowering interest rates on Greek debt, lengthening the deadlines for debt repayments, allowing Greece to buy back its bonds at a steep discount, and asking the European Central Bank to return profits made on Greek bonds.
But many analysts agree that at some point, Greece’s official lenders will have to take politically unpalatable losses, or haircuts, on their holdings of Greek debt in order to keep the country in the euro area, even if a range of other measures is taken to reduce the size of the state deficit and reform the economy.
Another critical challenge for the Eurogroup was smoothing over differences among the troika of lenders — the European Commission, the European Central Bank and the International Monetary Fund — about how quickly Greece should be obliged to bring its towering debt under control.
In a public disagreement last week at the previous Eurogroup meeting, Ms. Lagarde insisted that Greece cut its debt to the fund’s target of 120 percent of gross domestic product by 2020 while Jean-Claude Juncker, chairman of the Eurogroup, recommended giving Greece until 2022, a position shared by Germany.
Arriving at the meeting on Tuesday, Ms. Lagarde emphasized the importance of the 2020 goal to her organization, which, under its rules, cannot continue lending unless Greece’s debt is deemed sustainable. Finding a solution was “our goal, our purpose and our mission,” she said.
The difference is a highly sensitive matter for Greece’s biggest creditors in the euro zone, and for Germany in particular.
German leadership is wary of political repercussions from higher costs that would result from meeting the 2020 deadline. The Greek debt is now estimated at 175 percent of G.D.P. and the economy could shrink again next year.
“We are narrowing our positions,” Mr. Juncker told reporters early on Wednesday morning referring to gulf between him and Ms. Lagarde on Greece’s debt prospects.
“We are very close to a result” and there was “no major stumbling block,” Mr. Juncker insisted.
Prime Minister Antonis Samaras of Greece, who is struggling to hold together an increasingly fragile coalition, hopes that a final push by Athens to tie up loose ends could help speed money for the two-year extension to the country’s fiscal adjustment period.
Finance Minister Yannis Stournaras said late Sunday that Athens had done its bit. “We are fully ready for Tuesday,” he said. “There are no outstanding issues on our side.”
James Kanter reported from Brussels and Niki Kitsantonis from Athens.