European governments and banks struggled to reconcile competing proposals for a second bailout of Greece on Monday, three days before leaders meet to prevent the crisis from spreading through the region.

The euro zone summit scheduled for Thursday in Brussels is likely to agree on a rescue of Greece, supplementing a 110 billion euro ($154 billion) bailout launched in May last year, a French government spokeswoman said.

But after three weeks of preparatory talks, it was unclear how a consensus could be reached for private owners of Greek government bonds -- banks, insurers and other investors -- to contribute by taking cuts in the face value of their holdings.

Imposing a small tax on all euro area banks is under active consideration as a possible alternative to more risky forms of private sector involvement, a source familiar with the talks said, confirming a German media report.

The source also said officials were considering ways to prevent fallout from the crisis from damaging global markets.

Fears of a chaotic Greek debt default pushed the euro down against other currencies. Bond yields of highly indebted euro zone governments rose. Italy's 10-year yield climbed more than 0.2 percentage point to a euro-era high.

Paul de Grauwe, a professor of international economics at Leuven University in Belgium who has informally advised European Commission President Jose Manuel Barroso, said politicians had delayed taking decisive action on Greece for so long that their options were narrowing quickly.

We've had solutions in the past, but we haven't grasped them, he said. Now it's too late for some of those solutions to work anymore; the opportunity has been lost.

RANGE OF OPTIONS

Officials are wrestling with a range of proposed options for Europe's bailout fund, the European Financial Stability Facility, to finance a voluntary buy-back or swap of Greek bonds, or possibly both. They would be conducted at a discount to the bonds' face value, helping to reduce Greece's 340 billion-euro mountain of sovereign debt.

But they could face technical and legal obstacles, in some cases requiring approval by national parliaments. They risk fuelling market instability if credit rating agencies respond by declaring Greece in limited default.

The source familiar with the negotiations said a tax on banks, which might substitute for those plans, could raise 10 billion euros a year, yielding 30 billion euros over three years -- the sum Germany and other countries have set as the benchmark for the private sector's contribution.

Asked whether it was unfair to make banks not exposed to Greek debt share the burden with those that do have exposure, the source said the tax could be structured to fall mainly on investors with the most exposure. He did not say how.

This has been discussed for a few weeks but never really got momentum. Lately it's been getting a bit more. The Germans say they are not against it. It would be a form of private sector involvement without the collateral damage of triggering a credit event or a selective default, the source said.

Any contribution by the private sector is unlikely to be nearly enough to solve Greece's problem. Analysts estimate its debt would need to be roughly halved, to 80 percent of gross domestic product, to make it manageable in the long run.

A bond swap might have the most impact.

A European Union official told Reuters any agreement on a swap this week would probably be quite small, merely paving the way for a debate on a bigger restructuring of Greek debt that would have to take place in a few months.

What we're talking about down the road is the need for a massive reduction in the debt burden, and they are just not ready to do that yet, said Guntram Wolff, deputy director of the Bruegel think tank and previously a senior economist at DG Ecfin, the European Commission unit dealing with the crisis.

It will require some form of substantial debt restructuring and you have to see who is going to take the hit, will it be the taxpayers or will it be the banks? To carry out such a move you need to prepare, and they don't have the time to prepare before Thursday.

BAILOUT

As part of the second bailout, officials have also been looking at other measures to help Greece, including up to 60 billion euros of additional emergency loans from European governments and the International Monetary Fund; steps to recapitalise Greek and European banks; and ways to stimulate Greek economic growth.

EU sources said there was a basic agreement on extending the maturities and lowering the interest rates for bailout loans extended to Greece, Ireland and Portugal. Greece's EU loans have maturities of about 7.5 years with a rate of 4 percent; their length might be doubled or even quadrupled and the rate cut by at least 0.5 percentage point.

But de Grauwe said the mood of financial markets was so negative that such a step might not help weak euro zone states regain the ability to fund themselves.

If that was to be a solution, it's a solution we should have implemented months ago, when it would have worked.

There has also been talk of expanding the 750 billion euro bailout facility the EU and the IMF created last year as the debt crisis erupted. The EU source said there probably would not be enough time to agree on the idea this week.

The source familiar with the negotiations said that to reassure global markets, governments were considering proposals to make the EFSF more flexible by, for example, allowing it to recapitalise banks or provide precautionary credit lines.

Euro zone leaders may issue a statement declaring Greece is a unique case, to try to convince private investors they will not be called on to help pay for bailouts of countries such as Ireland and Portugal. After recent credit rating downgrades, however, many investors are assuming the worst.

IMF

Another concern is that the IMF and major non-European governments may lose patience with Europe.

German newspaper Die Welt quoted diplomatic sources as saying the IMF was angered by Europe's unsuccessful crisis management and that influential parties in the Fund wished not to take part in further bailouts of Greece. It did not elaborate.

U.S. Treasury Secretary Timothy Geithner said on Monday that Europe had to act more forcefully to contain risks in its banking sector, which is heavily exposed to Greek, Irish and Portuguese sovereign debt.

Geithner's Canadian counterpart also sounded the alarm.

Europe's debt problem will get harder and more expensive to solve unless European leaders act aggressively to deal with it, Canada's Jim Flaherty told Reuters.

Former U.S. Treasury Secretary and White House adviser Lawrence Summers, writing in a column contributed to Reuters, recommended steps, including sharp cuts in interest paid on bailout loans, allowing countries to buy EU guarantees for their issues of new debt and options for private investors.

It is to be hoped that European officials can engineer a decisive change in direction but if not, the world can no longer afford the deference that the IMF and non-European G20 officials have shown toward European policymakers over the last 15 months, Summers wrote.

Many economists think some form of regional guarantee for countries' debt along the lines suggested by Summers -- or perhaps even the issuance of joint euro zone bonds -- may ultimately be the only way to emerge from the crisis without one or more weak states being forced out of the bloc.

Germany has shown no appetite for such a solution, which in any case would require a complex revision of the EU treaty. Berlin worries that a common bond would provide no meaningful incentives for national governments to pursue prudent policies.

(Writing by Andrew Torchia; Editing by Ruth Pitchford)