The crisis plan approved by European leaders early Thursday set off celebrations on global stock markets and led officials to assert that they had turned a corner in the battle to rebuild confidence in the euro region.

But many market analysts cautioned that the 15-page plan, hammered out over late-night brinkmanship in a government office building in Brussels, remains a work in progress. Key details are uncertain, they say, and a slowing European economy could throw the program off course.

In the flush of their 3 a.m. announcement of a breakthrough in marathon negotiations, European officials made claims for the program that ranged from the grand to the unverifiable.

Greek Prime Minister George Papandreou said the expected 50 percent cut in what the country owes to banks and other private lenders had lifted “a burden from the past” and will give his country financial breathing room. French President Nicolas Sarkozy said the program would provide $1.4 trillion to prop up Spanish and Italian bonds, though details on the mechanics of that were scant.

Still, the plan seemed to begin untying the knots at the center of the euro region’s troubles: Banks will get fresh capital from private sources or taxpayers; weakened governments will have more help to hold down their borrowing costs; Greece will get outright debt relief and more time to overhaul its economy.

The region also committed
itself to reigniting economic growth, considered critical for the plan to work.

The United States has been pushing for the region to act more forcefully to resolve the debt crisis. The Obama administration had urged some more dramatic and fast-acting fixes that European officials rejected.

On Thursday, President Obama said the new plan provides “a critical foundation for a comprehensive solution to the euro-zone crisis.” But, after watching the problems of Greece fester into a global threat, Obama also emphasized that follow-through is crucial. “We look forward to the full development and rapid implementation” of the bailout plan, he said.

Major European exchanges jumped anywhere from 3 to 6 percent Thursday; stocks of banks in France and Germany soared close to 20 percent in some cases after a summer in which investors shunned European financial companies. U.S. markets also surged Thursday — the Standard & Poor’s 500-stock index advanced 3.4 percent, and the Dow Jones industrial average closed the trading session up 2.9 percent.

Asian markets also shot higher in early Friday trading. Japan’s Nikkei 225 index, up 1.4 percent at midday, rose above the 9,000 mark for the first time in eight weeks.

“Even if it probably was not the final word on the crisis, it is again another important step in the right direction,” analysts from ING said in a research note that conveyed a widely held feeling that the program was constructive but will need time before its impact is clear.

The headline feature — the 50 percent cut in the face value of roughly $240 billion in Greek bonds held by banks, pension funds and other investors — must still be finalized in follow-up talks to take place by year’s end.

And it’s uncertain whether the investors will volunteer to take the Greek bond losses to avoid credit agencies declaring a Greek default, which could again destabilize markets.

Emerging details made it seem that, for investors, it’s far from a free choice. In remarks to journalists as the meetings concluded, Luxembourg Prime Minister Jean-Claude Juncker said that a banking trade group agreed to the “haircut” after being told that their bonds would otherwise be wiped out through “the total insolvency of Greece.” Juncker said the ultimatum was “fiercely delivered” by himself, Sarkozy and German Chancellor Angela Merkel.

Charles Dallara, managing director of the Institute of International Finance and the chief negotiator for major banks, issued a statement just before midnight in Brussels saying there was “no agreement on any element of a deal.” Four and a half hours later, he welcomed the new plan and said financial institutions would help enact “a concrete voluntary agreement” to reduce Greece’s privately held debts by half.

In Germany, politicians and commentators reacted with an air of triumph, since the framework bore most of the country’s demands and few concessions.

“Merkel Triumphant,” read the headline on the Web site of the Bild tabloid, which has campaigned against spending German money on the bailout. “After ten hours of a Euro-nail-biter, Merkel comes out on top,” it said.

And a top German finance official, Jörg Asmussen, bragged that the agreement “clearly has German handwriting,” saying that the European Central Bank would remain “independent” by not serving as a lender of last resort, a key German demand.France, long Germany’s partner in key European decisions, had hoped for smaller losses for banks and was less concerned about attaching strings to the commitments made Thursday morning.

Sarkozy explained himself in an unusual 75-minute-long prime-time appearance on two of France’s top television stations.

“There’s a very painful history between Germany and France,” Sarkozy said in the appearance. “If we hadn’t agreed with Angela Merkel, Europe would not have survived.”

Some here credit the International Monetary Fund’s growing pressure on the finance leaders to offer broad debt relief as Greece’s finances began slipping into crisis and its economy began sliding deeper into recession. An IMF analysis of the situation presented European officials with a clear choice: Impose losses on the private sector and acknowledge that a euro-region nation could not repay its loans, or kick in additional tens of billions of dollars in taxpayer money to keep the country afloat.

The report informed several days of discussions leading into Wednesday’s summit.

“I think Greece owes a big thank you to the IMF” for bringing the issue to a head, said Miranda Xafa, an investment adviser at IJ Partners in Athens and a former Greek representative to the IMF board.

IMF managing director Christine Lagarde said the private losses were “of utmost importance” in stabilizing Greece’s finances. The losses are much steeper than those negotiated over the summer by the International Institute of Finance in a plan that eased Greece’s cash needs but did not actually cut the face value of bonds that the nation owes. The plan by the IMF and European officials will reduce the face amount.

Details are also sketchy on how to best use the euro region’s new bailout fund, the European Financial Stability Facility. The plan says that officials will consider using the fund’s roughly $600 billion to partially insure bonds issued by countries that face higher borrowing costs and will consider whether money can be raised for European bond investments through a new special investment fund. Eyes were turning east, hoping that China — whose leaders arrive in France next week for a Group of 20 summit — might invest.

But European officials acknowledged that the workings of the bailout fund were still being developed and that its success as a financial backstop for Italy or other large countries depends on whether investors can be lured back to the euro zone.

A plan to raise capital for banks will also take months to put in place and might force some already indebted nations such as Italy to borrow more to help their financial systems.

Staff writer Michael Birnbaum in Berlin contributed to this report.

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