European finance officials struggled to find ways to resolve Greece's debt crisis on Monday as sharply rising bond yields in Italy, the euro zone's third largest economy, added to the sense of urgency.

One senior European Union official said the situation had become almost entirely a political rather than an economic crisis, with parties taking firm, irreconcilable positions.

We've painted ourselves into a corner. At this point, either someone -- Germany, the ECB (European Central Bank) -- has to fundamentally shift position, or everything blows up, the official, who declined to be named, told Reuters.

The euro sank 1.6 percent against the U.S. dollar to its lowest level in six weeks and markets around the world moved in response to fears that Greece might eventually default. U.S. Treasury bonds rose sharply as investors sought safer assets.

EU sources said the 17 euro zone finance ministers were discussing the possibility of organizing a buy-back of Greek sovereign debt, or of asking private investors to swap their bonds for debt with longer maturities.

Germany, the Netherlands, Austria and Finland are determined that banks, insurers and other private holders of Greek debt should bear some of the cost of a second bailout of Greece, which would total around 110 billion euros ($154 billion).

But after weeks of negotiations with bankers, there has been next to no progress on agreeing a formula acceptable to all sides. A complex French proposal for investors to buy new Greek bonds as their existing ones mature appears to be floundering.

Meanwhile, the ECB has insisted it will not accept any scheme that credit rating agencies term a default, further limiting policymakers' options and making any bond swap extremely difficult to arrange.

A proposal to have the euro zone's bailout fund buy Greek government bonds from the market, or lend Greece money to conduct a buy-back, might take too long to push through the region's national parliaments, and has in any case run into opposition from Germany, the region's richest country.

I think it's problematic, a source familiar with German thinking told Reuters, referring to the buy-back idea.

There, you are not talking about participation of the private sector, you are talking about participation of the public sector. It doesn't give you a great bang for your buck.

As the policy stalemate has dragged on over the last several weeks, European markets have become increasingly jittery about the possibility that Greece might be forced into a disorderly default on its debt. This prospect has pushed up bond yields around the euro zone's weak economies.

A senior EU source said there was a strong possibility that another meeting of euro zone finance ministers would be called for the end of July, with the intention that this meeting would sign off on the Greek bailout.

ITALY

Officials say there is a new sense of urgency after Italy came under market attack last week.

The cost of insuring Italian debt against default jumped to a record high on Monday, while the spread of Italy's 10-year bond yield over German debt widened to a euro-era high of 3 percentage points. The yield jumped 0.44 percentage point -- the kind of sharp rise seen in Greece's bonds when the crisis there erupted last year -- to above 5.7 percent, an area which some bankers say may start putting heavy pressure on Italy's finances.

The bond sell-off has fanned fears that Italy, with the euro zone's highest sovereign debt relative to its economy after Greece, could be dragged into crisis. If that happened, the zone's bailout fund, the European Financial Stability Facility, would be too small to finance a multi-year bailout of Italy.

After talking by telephone to Italian Prime Minister Silvio Berlusconi, German Chancellor Angela Merkel said on Monday that Rome needed to demonstrate it was undertaking budget reforms necessary to restore confidence, and that she was confident it would do so.

Before Monday's euro zone finance ministers' meeting, Herman Van Rompuy, the president of the European Council, met ECB President Jean-Claude Trichet and Jean-Claude Juncker, the chairman of the finance ministers, for talks in Brussels.There was no sign this meeting achieved any breakthrough.

The market pressure on Italy is due partly to its high sovereign debt and sluggish economy, but also to concern that Berlusconi may try to push out his longtime finance minister Giulio Tremonti, who has promoted deep spending cuts to control the budget deficit.

(Additional reporting by John O'Donnell, Leigh Thomas and Luke Baker in Brussels, Silvia Westall in Vienna, Stephen Brown in Berlin and Milan/Rome bureaus; Writing/Editing by Mike Peacock and Andrew Torchia)