It was approaching 2 a.m. Thursday, not long before the Asian markets would open, and the two leaders were desperately trying to nail down the last component of a complex deal to save the euro: forcing the banks to pay a greater share of Greece’s effective default.

For hours, negotiators had been trying to persuade the banks to accede to a “voluntary” 50 percent loss in the face value of their Greek bond holdings. The banks, which had already agreed to a 21 percent write-down, had dug in their heels.

They knew how badly the European leaders needed a deal, and how much financial experts feared a disorderly, involuntary default. That could set off a “credit event,” throwing world financial markets into turmoil, much as the collapse of Lehman Brothers did in the fall of 2008.

But Mrs. Merkel called the bankers’ bluff, said officials present at the discussions. Accept the 50 percent write-down, she told the bankers, or bear the consequences of default. In effect, she was willing to risk a credit event, and to place the blame for any fallout on them.

The European success sent the markets soaring and laid out the path to a more comprehensive solution to the euro crisis, though the plan faces hurdles.

It includes an order to weak banks to raise more capital to protect against bad loans, and an effort — still very vague — to increase the firepower of the $625 billion bailout fund, the European Financial Stability Facility, to better protect large and vulnerable economies like Spain and Italy.

But the very process of achieving those steps underscored the many problems that lie ahead for the euro zone. While the rescue package has been hailed as an important step, it was achieved only under enormous pressure from the financial markets and with a steely, last-minute stand by Mrs. Merkel.

Foremost among those problems is Italy, which is too big to bail out, owing a total of $2.7 trillion, or 120 percent of its gross domestic product. While Italy runs a relatively small budget deficit, Prime Minister Silvio Berlusconi’s government seems paralyzed, vowing structural changes to produce growth and to further shrink public spending, but it is so far too weak and divided to deliver on most of its promises.

Italian news outlets reported on Thursday that a number of lawmakers from Mr. Berlusconi’s coalition had signed a letter asking him to stand down to allow for the creation of a government that could pass the measures that would tranquilize jittery financial markets.

Market skepticism about Italy has led to high interest rates on its bonds, which if unchecked could rip huge holes into its budget and possibly provoke a full-blown credit crisis. With Mr. Berlusconi hanging on by a thread, and his coalition partner, Umberto Bossi of the Northern League, working to block fundamental change, Italy remains a major vulnerability in restoring market confidence to the euro.

European leaders Thursday welcomed new promises made by Mr. Berlusconi, including a weak pledge to increase the age for pensions to 67 from 65 by the year 2026, but said sternly that carrying them out was the key.

Along with the European Central Bank, they have demanded such changes in return for buying up Italian bonds at cheaper than market rates and helping to create the bailout fund, and now to expand it to about $1.4 trillion, because at $625 billion it is far too small to protect Italy or Spain, and nearly half of that is already committed.

But the leaders were vague about how to enlarge the fund, and reluctant to put up more of their own nations’ capital. They said they hoped to create another special fund open to investment by China, Russia and Japan — which all expressed a willingness to help in principle — as well as by other wealthy nations with surplus cash. But how such a fund would work, and what guarantees it would provide to investors, remain to be determined next month, European officials said. Until the details are clear, there is likely to be little investment.

Also left unclear are the details of how to leverage the existing fund, by guaranteeing a percentage of potential losses by bondholders. While Mr. Sarkozy said the aim was to leverage the fund up to $1.4 trillion, there was no agreement on the specific percentage the fund would guarantee. More should become clear by the time of the Group of 20 summit meeting on Nov. 3 and 4 in Cannes, France.

Even the Greek deal is considered not sufficient. By 2020, Greece, if all goes to plan — which so far it has not — will still have a debt of 120 percent of gross domestic product, the same figure that has everyone so worried about Italy. So Greek pain will continue as it tries to restart growth while balancing its budget and paying even this amount of accumulated debt. Even the write-down in the face value of Greek debt is problematic because it does not cover all of the country’s outstanding public debt, with the rest controlled by institutions that will not take part in the restructuring.

Liz Alderman contributed reporting from Paris, and Elisabetta Povoledo from Rome.

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