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Officials said leaders had reduced seven different proposals down to two options that are not mutually exclusive. Both options essentially would use the European Financial Stability Facility to insure investors against a first round of losses on bonds from wobbly countries.

But before that can be done, those countries have to persuade their partners in the eurozone that their weakness is only temporary and they can get back into shape soon.

German Chancellor Angela Merkel and French President Nicolas Sarkozy came out with particularly strong words for Italy.

“We made it very clear that Italy is a big and important partner for the euro area and that everything needs to be done to live up to this responsibility,” Mrs. Merkel told reporters after the two met with Mr. Berlusconi.

“Trust does not just come from a firewall,” she added. “Italy has great economic power, but Italy also has a very high overall debt level. And that was to be taken down in the coming years in a credible way.”

The stern tone reflected the seriousness of Europe’s problems, which have roiled financial markets in recent months and been blamed for slowing economic growth across the globe.

Worst off, of course, is Greece, which is reeling from repeated rounds of budget cuts, job cuts and new taxes that have sparked near-daily strikes and even riots. The country is looking at a fourth year of recession, and unemployment has hit a record of 16.5 percent.

Greece has proven again and again that we are making the necessary decisions to make our economy sustainable,” Greek Prime Minister George Papandreou told reporters Sunday. “But it’s been proven now that the crisis is not a Greek crisis. The crisis is a European crisis, so now is the time that we as Europeans need to act.”

To ease the pressure, banks will be asked to accept much bigger losses on Greek bonds.

Austrian Chancellor Werner Faymann said the cut in the value of Greek government bonds likely will be raised “in the direction of 40 to 50 percent.”

“A cut in the debt is the right step,” Mr. Faymann told the Austrian newspaper Wiener Kurier.

Despite massive budget cuts and reforms, a new report says Greece’s economic situation is still dire and it could take the country decades to emerge from the crisis.

The eurozone has accepted that it will have to provide Greece with tens of billions of euros in extra aid — on top of 110 billion euros ($152 billion) granted in May 2010. But to keep a lid on that amount, banks must go far beyond a preliminary deal reached in July, in which they promised take a cut of 21 percent of their Greek bondholdings.

The near-consensus among eurozone countries that Greece’s debt will have to be slashed is one of the reasons banks across Europe — not only in the 17-country eurozone — will be forced to shore up their capital buffers in the coming months.

To that end, Mr. Sarkozy said the EU will require banks to raise their capital buffers to higher levels by 2012 rather than the 2019 laid out under the Basel III banking rules.

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