Details of the agreement were not disclosed.

Released by the office of the French president, Nicolas Sarkozy, the statement said he and Chancellor Angela Merkel of Germany had reached an agreement they presented to Herman Van Rompuy, president of the European Council, for consideration.

The leaders of the 17 member countries of the euro zone are to meet in Brussels to try to keep the debt crisis from spiraling out of control after a week of market turbulence in which borrowing costs spiked in Italy and Spain.

Many see the 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, and who, earlier this week, played down expectations of a breakthrough on Thursday.

“Nobody should be under any illusion: the situation is very serious,” José Manuel Barroso, president of the European Commission, the executive arm of the European Union, said earlier in the day. “It requires a response. Otherwise the negative consequences will be felt in all corners of Europe and beyond.”

The commission was arguing for a plan that would have private creditors swap Greek bonds that mature before 2019 for new 30-year bonds, thereby prompting a selective default, according to an official briefed on the negotiations who was not authorized to speak publicly.

The terms of the plan would imply a 20 percent reduction in the value of Greek bonds, the official said, a change that would raise tens of billions of euros to be directed to support the Greek bailout.

In addition, the other countries in the euro area and the International Monetary Fund would contribute 71 billion euros, or $100 billion, to the rescue plan, up to 2014.

Meanwhile, a tax on the banks equivalent to 0.025 percent of the assets of financial institutions could raise around 50 billion euros over five years and would finance a buyback of Greek bonds 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.

Although a tax on banks has been discussed for several days, it had previously been presented as a tool for raising private sector financing without provoking a default, rather than a means of raising additional money. There are also technical problems with a bank tax that 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.

With its willingness to contemplate selective default and ambitious targets for raising cash from the private sector, the European Commission proposal seems to be intended to appeal to Germany, which has consistently called for banks to take a substantial part of the loss.

Germany, Finland and the Netherlands are at odds with the European Central Bank 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. That may require measures to ensure that liquidity still flows to Greek banks, the official said.

Officials said it was unclear whether the plan floated by the commission would be accepted by Berlin and Paris and other governments.

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.

The European Financial Stability Facility looks destined to gain a more important role, financing the buyback of bonds, and possibly the extension of credit lines or help in bank recapitalization.

“For the federal government, the participation of private investors is of immense value and is our aim,” Steffen Seibert, the German government spokesman said on Wednesday. “We are very confident that there will be a good and sensible solution,” he said in Berlin.

Economists said that a debt buyback would have other consequences.

If the program were voluntary, some investors might not participate, hoping that market prices for Greek debt would rise. So the buyback would have to be compulsory — a default, in other words — for Greece to get the debt reduction it needed, said Harald Benink, a professor of banking at Tilburg University in the Netherlands.

In addition, Greek banks would need to be bailed out because they have such large holdings of domestic debt. Portugal and Ireland might need a similar buyback deal to protect them from market attacks. The European Central Bank might need to be compensated for losses on its holdings of Greek debt.

And the European Union would have to substantially increase the size of the stability fund to show markets it is ready to protect Spain and Italy, Mr. Benink said.

“That requires a lot of political willingness and ability,” he said. “The worry is that these political leaders will have to drive at a much faster speed than their voters will allow them.”

Judy Dempsey reported from Berlin. Jack Ewing in Frankfurt and Matthew Saltmarsh in London contributed reporting.

This article has been revised to reflect the following correction:

Correction: July 22, 2011

An article on Thursday about efforts to negotiate a rescue plan for Greece paraphrased incorrectly, in some editions, from a statement by the French president, Nicolas Sarkozy, about the progress of talks. Mr. Sarkozy said that Germany and France had agreed on a plan to be presented to a summit meeting; he did not say that the plan would include the participation of Europe’s banking sector. The article also misspelled part of the surname of the president of the European Council, who received the agreement. He is Herman Van Rompuy, not Van Rumpuy.

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