By Luke Baker and Julien Toyer
Under the deal, the private sector agreed to voluntarily accept a nominal 50 percent cut in its bond investments to reduce Greece's debt burden by 100 billion euros, cutting its debts to 120 percent of GDP by 2020, from 160 percent now.
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At the same time, the euro zone will offer "credit enhancements" or sweetners to the private sector totaling 30 billion euros. The aim is to complete negotiations on the package by the end of the year, so Greece has a full, second financial aid program in place before 2012.
The value of that package, EU sources said, would be 130 billion euros -- up from 109 billion euros when a deal was last struck in July, an agreement that subsequently unraveled.
"The summit allowed us to adopt the components of a global response, of an ambitious response, of a credible response to the crisis that is sweeping across the euro zone," French President Nicolas Sarkozy told reporters afterwards.
As well as the deal on deeper private sector participation in Greece -- which emerged after Sarkozy and German Chancellor Angela Merkel engaged in the negotiations with bankers -- euro zone leaders also agreed to scale up the European Financial Stability Facility, their 440 billion euro ($600 billion) bailout fund set up last year.
Leaders hope that will be enough to stave off any worsening of the debt problems in Italy and Spain, the region's third and fourth largest economies respectively.
Riskier assets across the board rallied in Asia, with stocks outside Japan up nearly three percent at 0600 GMT (2 a.m. EDT) in response to the agreement. The euro hit a seven-week high.
Earlier, U.S. stocks rallied after news emerged of the intention to boost the power of the EFSF fund.
The EFSF will be leveraged in two ways, either by offering insurance, or first-loss guarantees, to purchasers of euro zone debt in the primary market, or via a special purpose investment vehicle that will be set up in the coming weeks and which is aimed at attracting investment from China and Brazil.
The methods could be combined, giving the EFSF greater flexibility, the euro zone leaders said.
"The leverage could be up to one trillion (euros) under certain assumptions about market conditions and investors' responsiveness in view of economic policies," said Herman Van Rompuy, the president of the European Council.
"There is nothing secret in all this, it is not easy to explain but we are going to more with our available money, it is not that spectacular. Banks have been doing this for centuries, it has been their core business, with certain limits."
PROOF OF THE PUDDING WITH MARKETS
Japan and Canada welcomed the euro zone agreement. China's official Xinhua news agency said the outcome was "positive but filled with difficulties."
As with the July 21 agreement, which quickly broke down when it became difficult to secure sufficient private sector involvement and market conditions rapidly worsened, the concern is that Thursday's deal will only work if the fine print can be promptly agreed with the private sector, represented by the Institute of International Finance.
Charles Dallara, the managing director of the IIF, said those he represented were committed to making the deal work.
"On behalf of the private investor community, the IIF agrees to work with Greece, euro area authorities and the IMF to develop a concrete voluntary agreement on the firm basis of a nominal discount of 50 percent on notional Greek debt held by private investors with the support of a 30 billion euro official ... package," he said in a statement.
"The specific terms and conditions of the voluntary PSI (private sector involvement) will be agreed by all relevant parties in the coming period and implemented with immediacy and force. The structure of the new Greek claims will need to be based on terms and conditions that ensure (net present value)loss for investors fully consistent with a voluntary agreement."
Euro zone leaders will be hoping the agreement, which will also be accompanied by a recapitalization of the European banking sector by around 106 billion euros, will finally draw a line under a crisis that has roiled financial markets and threatened to tear apart the euro single currency project.
"It's great news that they've managed to increase the bail-out fund to 1 trillion euros plus agree on some sort of haircut arrangement for the private investors in Greek debt.
"The problem is, we don't actually know how they are planning to increase the bail-out fund size from 440 billion euros to a trillion. On top of that, there are some questions as to whether one trillion euros in itself is enough."
Jose Manuel Barroso, the president of the European Commission, said the final details on the Greek package, which follows a program of 110 billion euros of loans granted to the country last year, would only be worked out by year-end.
And EU finance ministers are not expected to agree on the nitty-gritty elements of how the scaled up EFSF will work until some time in November, with the exact date not fixed.
As part of efforts to attract investors into the special purpose vehicle attached to the EFSF, Sarkozy said he would talk to Chinese President Hu Jintao in the coming days. Beijing has so far been a big buyer of bonds issued by the EFSF, which is triple-A rated by credit agencies.
Prime Minister Silvio Berlusconi has promised to raise the retirement age to 67 by 2026, and pursue other adjustments to the country's economic model, steps the EU praised but said would only be positive if they were implemented.
"The key is implementation. This is the key. It is not enough to make commitments, it is necessary now to check if they are really implementing," said Barroso.
(Additional reporting by Julien Toyer, Jan Strupczewski, Yann Le Guernigou, David Brunnstrom, Robin Emmott, Harry Papachristou and John O'Donnell in Brussels, Annika Breidthardt and Sarah Marsh in Berlin, Daniel Flynn in Athens, Barry Moody in Rome; Writing by Luke Baker and Mike Peacock; editing by Janet McBride)