Details of the agreement, reached early Thursday in Berlin after seven hours of talks, were not disclosed. The talks had centered on the role private investors and banks would have to play in stabilizing Greece’s finances and reducing a debt burden that threatens to stifle any prospect of economic recovery.

A statement from the French president, Nicolas Sarkozy, and the German Chancellor, Angela Merkel, said they had “listened” to the views of the president of the European Central Bank, Jean-Claude Trichet, who flew in from Frankfurt unexpectedly to join the meeting.

Though it did not say if they had settled the issue of whether Greece should be allowed to write down some of its debt — something Mr. Trichet has argued publicly and adamantly against — suggestions ahead of the summit meeting in Brussels were that the E.C.B had softened its stance.

“The demand to prevent a selective default has been removed,” the Dutch Finance Minister Jan Kees de Jager told the Dutch parliament in The Hague, Reuters reported.

Were Mr. Trichet to accept a temporary default, the euro-zone leaders may have to consider new ways to ensure that Greek banks could access funding that they currently receive from the E.C.B, possibly by guaranteeing Greek bonds themselves for a short period.

The euro and European stocks rallied on news of a potential deal, while the risk premium investors demand to hold the weaker euro zone bonds rather than benchmark German ones fell.

The French-German agreement was being presented to the other leaders of the 17 member euro zone in Brussels. The summit meeting was called after days market turbulence in which borrowing costs spiked in Italy and Spain, raising fears the euro debt crisis would spread to those, much bigger countries, potentially setting off another global financial crisis.

Representatives of big European banks were said to be in Brussels in parallel meetings, said one official not authorized to speak publicly.

Germany, Finland and the Netherlands have been at odds with the E.C.B. and some governments over their insistence that private bondholders share the pain. Besides concerns over contagion, the central bank has said that a selective default would make it impossible to accept Greek bonds as collateral.

“Selective default” is a term used by credit rating agencies when the terms of a bond, such as the repayment deadline or interest rate, have been altered. It falls short of an outright default rating, which is usually triggered when the borrower stops making payments.

Many saw the summit meeting as a moment of truth, particularly for Mrs. Merkel, whose caution has been blamed by some for the region’s failure to stem the crisis.

The central elements of the package are expected to be a buyback of Greek bonds, probably financed via the euro zone bailout fund known as the European Financial Stability Facility, the official said. That would reduce the stock of Greek debt by around 20 percentage points of gross domestic product.

The official said the final statement from the summit meeting would remain relatively vague on the exact extent that banks will “voluntarily” participate in the bailout, for fear that too much commitment now on might spook credit rating agencies, according to another euro area official involved in the talks, who also was not authorized to speak publicly. Details of the private sector involvement will be communicated at a later date, he said.

European leaders are not expected to increase the size of the E.F.S.F., although such a step is not being ruled out for the future, the second official said.

But the final statement is likely to include details of a plan to assist Greece as well through the transfer of more European Union funds earmarked for development, based around infrastructure spending, the official added.

Another element being considered was a plan that would have private creditors swap Greek bonds that mature in the next few years for longer-term ones, but it was less clear if that would be adopted.

Officials suggested that an earlier proposal for a tax on banks had been dropped. This was once seen as a tool for raising private sector financing without provoking a default but posed technical problems since the tax would have to be levied by each national government and would exclude countries that did not use the euro even if they had Greek liabilities.

Asked about the bank tax idea Jean-Claude Juncker, the prime minister of Luxembourg and head of the Eurogroup of finance ministers, said: “I don’t think that there will be an agreement on that.”

In all the Commission wants the euro area and the International Monetary Fund to contribute 71 billion euros, or $100 billion, to the rescue plan, up to 2014.

One element attracting consensus is the need to reduce the burden on indebted nations, not only by buying back Greek bonds but also through a reduction in the interest rates offered to Greece, Ireland and Portugal, which have also accepted international help. The maturities of these loans would also be extended.

As part of the Greek package, Ireland and Portugal — the other two euro countries that have received international bailouts — will receive new, similarly favorable financing conditions on their official loans, the second official said, meaning that they would have to pay the E.F.S.F.’s borrowing rate plus some costs, which are all expected to come in around 3.5 percent.

Ireland will not be required to raise its relatively low corporate tax rate, currently 12.5 percent, as some countries, such as France, had sought, the official said.

“They will have a lower interest rate and extended maturities without giving up anything,” the official said.

Matthew Saltmarsh in London contributed reporting.

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