German Chancellor Angela Merkel called on Sunday for private investors to make a major contribution to bailing out Greece, as pressure rose for radical action to cut the country's debt burden.

Officials proposed a range of schemes for Europe's bailout fund, the European Financial Stability Facility, to finance a buy-back or a swap in which private owners of Greek government bonds -- banks, insurers and other investors -- would accept cuts in the face value of their holdings.

European Central Bank Executive Board member Lorenzo Bini Smaghi suggested the EFSF be allowed to provide funds for a buy-back of bonds from the market, where prices have in some cases fallen 50 percent from levels at which the debt was issued.

This would allow the private sector to sell bonds at market prices, which are currently below nominal value. At the same time, the public sector could benefit monetarily, Bini Smaghi told Sunday's To Vima newspaper in an interview.

Wolfgang Franz, head of Germany's wise men economic advisers to the government, said the huge size of Greece's 340 billion euro ($480 billion) debt pile meant it was inevitable and justified for the private sector to accept losses.

One possibility would be that the current EFSF euro rescue mechanism swaps -- at a significant discount -- Greek bonds into bonds it issues and guarantees, Franz was quoted as telling Focus magazine at the weekend.

Alarmed by the spread of market jitters over Greece to Italy and Spain, where bond yields have surged in the past 10 days, European governments are struggling to put together a second bailout of Greece that would supplement a 110 billion euro rescue launched in May last year.

Germany is insisting private investors be involved in the second bailout, and Merkel indicated on Sunday that if they did not voluntarily agree to a major contribution now, they might eventually be forced into a more costly solution to the crisis.

The more we can involve private creditors now on a voluntary basis, the less likely it is that we will have to take next steps, Merkel told public broadcaster ARD without elaborating on what those steps might be.

Three weeks of talks between European officials and the private sector have failed to reach a deal on the second bailout of Greece, but the lobby group representing commercial banks said on Sunday that some progress had been made.

Progress has been made and the discussions are continuing, the Institute of International Finance said in a brief statement. It said the talks were focusing on several options related to Greece's financing needs and longer-term debt sustainability.

Last week, European Council President Herman Van Rompuy announced that euro zone leaders would hold a summit in Brussels on Thursday this week to discuss the rescue of Greece.

But Merkel, while describing the summit as urgently necessary, said she would only attend if lower-ranking officials had already prepared a clear rescue plan. I will only go there if there is a result, she said.

BUY-BACK

Other options on the table include an extension of the maturities of Greek bonds. But German weekly magazine Der Spiegel, citing finance ministry sources, reported at the weekend that a debt buy-back had become the option most likely to attract a consensus.

Greece could cut its public debt by 20 billion euros if it bought back its sovereign bonds at market prices as part of a rescue deal, the magazine said.

Legal and technical obstacles may lie in the way of any step to involve the private sector in helping Greece. Bini Smaghi acknowledged, for example, that current EFSF rules did not provide for it to buy bonds from the secondary market; changing the rules might require approval by national parliaments.

Another potential obstacle is the ECB, since the central bank's president Jean-Claude Trichet has opposed any measure that would cause credit rating agencies to declare Greece in default, even on a limited basis.

But in an interview to be published on Monday, Trichet held out the possibility that a default could be managed smoothly. He said the ECB would stop accepting defaulted bonds as collateral in its money market operations -- a blow to Greek banks which depend on the operations for funding -- but suggested governments might provide other collateral.

The governments would then have to step in themselves to put things right...The governments would have to take care the Eurosystem is presented with collateral that it could accept, Trichet told the Financial Times Deutschland without elaborating.

A deal on a private sector contribution to Greece would probably not by itself come close to solving the problem; officials and private economists estimate the country's debt would have to be cut by about half, to 80 percent of gross domestic product, to make it manageable in the long term.

As part of the second bailout, officials are also 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 economic growth in Greece.

As a key shareholder in the IMF, the United States is important to continued IMF support of Greece. U.S. Secretary of State Hillary Clinton, visiting Athens on Sunday, voiced support for Greece's effort to overcome its crisis, saying it was taking hard steps needed for future growth.

But former U.S. Treasury Secretary Lawrence Summers, writing in a column contributed to Reuters, said Europe needed to act much more aggressively than it had done so far to prevent the Greek crisis from damaging both the region's single currency and the global economic recovery.

He recommended steps including sharp cuts in interest paid on bailout loans, allowing countries to buy European Union guarantees for their issues of new debt, and a menu of options for private investors to become involved.

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.

Also on Sunday, Portuguese Prime Minister Pedro Passos Coelho said his government would impose additional spending cuts in the next four weeks to address a budget slippage it had discovered and meet the target for cutting its budget deficit under a 78 billion euro bailout by the EU and the IMF.

He said the slippage of some 2 billion euros would be partly covered by an extraordinary tax which the government had already announced that would bring 1.25 billion euros to state coffers. The rest would come from spending cuts.

(Writing by Andrew Torchia; Editing by Jon Boyle)