BRUSSELS — European countries will force their largest banks to quickly increase their capital buffers as part of a grand strategy to solve the continent's debt troubles, but leaders gathered at a crisis summit struggled to agree on the other key parts of the plan.

Strengthening Europe's banks is key to finally getting a grip on the debt crisis that has roiled the continent for almost two years and threatens the future of the euro, the common currency that is at the heart of Europe's postwar unity.

Fears that financially weak countries like Greece, Ireland and Portugal — and even larger economies like Italy and Spain — could default on their borrowings has eroded confidence in Europe's banks, which own much of those countries' debt in the form of bonds.

The hope is that forcing banks to value those bonds close to what they would sell for on the market, and at the same time make them expand their rainy-day funds, will help prevent a credit crunch similar to the one created in 2008 by the collapse of U.S. investment bank Lehman Brothers.

However, the plan to recapitalize banks, much of which had been known for several weeks, was the easiest part of a broader package designed to end the debt crisis.

Leaders of the 17-country eurozone continued to fight over two other elements — reducing Greece's massive debts and increasing the firepower of the eurozone's bailout fund so it can effectively stop the crisis from spreading.

The fear is that more delays and half-baked solutions could push not only Europe, but much of the rest of the developed world back into recession, eliminate hundreds of thousands of jobs and eliminate decades of bringing Europe's once-warn torn nation states closer together.

"Our challenge today is not simply to save the euro. It's to safeguard the ideals we cherish so much in Europe: peaceful cooperation amongst our nations, social cohesion and solidarity without prejudice amongst our people," said George Papandreou, the prime minister of Greece, whose country kicked off the continent's debt drama almost two years ago.

Greece's debt — on track to top 180 percent of economic output — was also the most fought-over issue at the summit.

Until now, the eurozone has failed to reach a deal with the country's private creditors, big banks and investment funds, to accept significant losses on their Greek bondholdings. That in turn has triggered disputes among the currency union's members.

German Chancellor Angela Merkel told lawmakers in Berlin that the goal was to bring Greece's debt down to 120 percent of economic output by 2020. That would imply a cut of more than 50 percent to the face value of Greek bonds and may be more than private investors would be willing to accept voluntarily.

Others, including France, the European Commission and the European Central Bank are in favor of a softer deal with banks, stressing that any solution will have to be voluntary to avoid creating even more market panic.

Merkel's Austrian counterpart Werner Faymann told reporters that a cut of "40 to 50 percent is part of the debate," signaling that even Germany's traditional ally was taking a more flexible stance.

Doubts also remained over the third and final issue on the table: How to give the eurozone's bailout fund, the €440 billion ($612 billion) European Financial Stability Facility, the firepower it needs to stop the crisis from engulfing large economies like Italy and Spain and help keep big banks from collapsing in the worsening market turmoil.

"I think that effectively, it has to be able to intervene a good deal beyond €1 trillion ($1.4 trillion)," Belgian Prime Minister Yves Leterme said of the bailout fund, also known as the EFSF.

Since states have ruled out boosting their financial commitments to the fund, the eurozone was working on two complex schemes that would allow the EFSF to act as an insurer for new bonds from wobbly countries like Italy and Spain.

If the fund promised to compensate investors against the first 20 percent or 30 percent of losses in the case of a default, that would make those bonds a much safer investments. Spending some €250 billion ($348 billion) on guarantees could under that scheme attract new lending of up to €1 trillion.

Figuring out those two parts of the plan — the cuts to Greek debt and the bailout fund — is necessary before the new rules on bank capital buffers can come into effect.

"A bank recapitalization without any remaining element — such as the firewall, to name one example — would not have any chance of success," said Polish Finance Minister Jacek Rostowski, whose country currently holds the revolving EU presidency.

By the end of June, the banks will need to have a core Tier 1 capital ratio of at least 9 percent, Rostowski said in a news conference after the 10 EU countries that don't use the euro left their colleagues to sort out the other problems. The core Tier 1 ratio measures how much good capital a bank holds compared with its risky investments.

The new capital threshold is much higher than the 5 percent capital ratio the banks had to prove in stress tests carried out just this summer.

On top of that, the new rules will require banks to fully account for all sovereign debt they hold. The banks' capital levels will be calculated only after they mark down the government bonds. In the July tests, they had been allowed to assume that at least some of the bonds from struggling countries would be paid in full.

DiLorenzo contributed from Paris. Juergen Baetz and Geir Moulson in Berlin; Raf Casert, Don Melvin and Robert Wielaard in Brussels; Karel Janicek in Prague, and Cecile Brisson in Paris also contributed to this report.