Nicolas Sarkozy arrives for an EU summit in Brussels. (AP Photo)

— Top European leaders convened crisis talks in Brussels on Thursday to try to put together a more durable financing plan for Greece and boost confidence about the stability and economic fortunes of the 17 nations that share the euro as a currency.

Agreement is considered critical to the direction of Europe’s economy and to the global recovery as well. The poor state of public finances in several European countries has been cited as a chief risk to the world financial system, and doubts about the ability of these countries to repay hundreds of billions of dollars in bonds have upset world markets for months.

But as the group gathered, they were also confronting an uncomfortable fact: The solutions being discussed might carry their own risks, including the possibility that they will cause Greece to be declared in default by the major world credit rating agencies.

At the core of the proposals under consideration are concessions by banks and other private bondholders to roll over maturing bonds and keep their money invested in Greece for years to come — lessening the country’s need for cash but likely causing a default declaration.

Although key figures such as European Central Bank president Jean-Claude Trichet have fought that outcome, it might be the only alternative that can produce a political accord among top euro nations such as Germany and France and also give Greece the financial room it needs to reinvigorate its economy.

“You can never exclude such a possibility,” Luxembourg Prime Minister Jean-Claude Juncker said as he headed into the session.

In comments before heading into the meeting, leaders indicated they were looking for what German Chancellor Angela Merkel referred to as a solution “at the root” -- one that acknowledges Greece is not likely to grow fast enough or produce enough tax revenue to pay off the more than $400 billion it has borrowed. Many economists have argued that the country is insolvent, and that programs which merely lend it more money without somehow cutting the overall amount owed were destined to fail

That’s the strategy followed until now, with the IMF and others insisting that Greece could be put back on track with some public loans and internal economic reform.

But as leaders gathered, the aim was to more deeply restructure Greece’s debts, finding ways to provide it money with lower interest rates, longer repayment terms and a break on the total amount owed -- like a homeowner rewriting an underwater mortgage.

In the Hague Dutch Finance Minister Jan Kees de Jager said that arguments against a narrow and well managed “selective default” had been “swept from the table,” and that leaders would “do something for the debt duration and also lower the debt burden,” wire services reported. As opposed to a general default, when a borrower simply misses payments on its debts, a selective default involves specific bonds. It can be a short-lived condition and ratings agencies have said that once they impose such a designation, they would factor the country’s improved condition into their analysis and possibly issue better ratings for future bond sales.

Major European stock markets closed sharply higher with the summit underway and expectations rising about the breadth of a possible deal. U.S. exchanges were also gaining ground.

In advance of the meeting, Merkel and French President Nicolas Sarkozy reached agreement on the outlines of a deal after hours of negotiations in Berlin on Wednesday, French officials said.

They have not released details, but French officials said Merkel and Sarkozy would deliver a “strong statement” at the summit. As heads of the euro area’s two largest economies, accord between them is important.

Default would mark a striking defeat for the collective efforts of Europe’s leadership, who for 18 months have tried to get ahead of a crisis of confidence that instead continued to spread.

Three euro-zone countries — Greece, Ireland and Portugal — are now under joint European-International Monetary Fund rescue programs, and there are signs that markets are beginning to lose faith in the much-larger economies of Spain and Italy, who because of their size could threaten broader world financial problems if they fall into trouble.

The crisis has been lingering so long that Greece needs a second bailout, estimated at another $140 billion for the next three years.

About $100 billion is expected to come in loans from other European countries, and $40 billion through concessions from private investors — an element Merkel has insisted on as head of the country that is making the largest contribution to the public loans.

But many analysts have argued that default needn’t be catastrophic and could in fact be short-lived and productive for the Greek and European economies if handled well. And European leaders seemed to be accepting that view.

A main stumbling block is Trichet, who as head of the ECB has said that he might have to stop providing funding to Greek banks if a default is declared — potentially creating a separate set of problems for Greece’s financial system.

However, reports from Brussels indicated an array of ideas were being discussed to work around that problem. An existing European bailout fund, for example, could be broadened to guarantee Greece’s bonds. The IMF in particular has pushed for a more liberal use of that existing fund.

Merkel has been insisting that banks and other private investors contribute to a solution, but her demand has been difficult to put into practice. Even if investors voluntarily accept less than the full value for their holdings of Greek bonds, ratings agencies have said it would constitute a default, an event that could touch off deeper financial problems within Europe and beyond.

Merkel has been counseling patience in the search for a longer-term fix, while others insist that disaster threatens if decisions are not made soon. She also has said she doubts the talks will produce the kind of “spectacular solution” that France and other euro-zone countries have been seeking.

The International Monetary Fund has warned that Europe’s problems could put the global recovery at risk if they undermine banks and financial institutions in the key European economies.

“Nobody should be under any illusion. The situation is very serious. It requires a response. Otherwise the negative consequences will be felt in all corners of Europe and beyond,” European Commission President Jose Manuel Barroso said at a news conference.

The Obama administration also has been monitoring events, concerned over prospects that the euro’s financial troubles could cause the sort of collapse in confidence that followed the failure of Lehman Brothers and contributed to the deepest economic downturn since the Great Depression.

Greek Prime Minister George Papandreou told Bloomberg News the meeting was a “make or break” moment for European leaders to prove they will stand behind troubled euro-zone countries.

A host of ideas are in play to give the euro that larger sense of financial stability.

They include expanding the uses of an existing bailout fund so it can be used to buy the bonds of countries that come under market pressure. Italy and Spain, for example, have seen their borrowing costs rise in recent days because of concern that their levels of public debt are not sustainable — and that the euro zone as a whole has not shown the resolve to back them up if they get into trouble. Purchases of their bonds with the bailout fund — paid for largely by Germany — would help keep their borrowing costs down.

Other ideas include the issuance of common “euro bonds” as a complement to each of the 17 nations issuing their own debt. Euro bonds, with the common backing of the currency union, would carry a lower interest rate, akin to those that top-rated countries such as Germany pay.

However, as with all of the proposed solutions, there are limits — so far — to Europe’s willingness to cooperate. In the case of euro bonds, it would put Germany’s good credit standing on the line to underwrite looser spending policies in places such as Greece and Italy.

For more coverage on the U.S. debt-ceiling showdown and the debt crisis in Europe, visit Post Business.