Euro zone finance ministers and the International Monetary Fund made their third attempt in as many weeks to agree on releasing emergency aid for Greece on Monday, with policymakers saying a write-down of Greek debt is off the table for now.

Greek Finance Minister Yannis Stournaras said he was confident the ministers would reach a deal after Greece fulfilled its part of the deal by enacting tough austerity measures and economic reforms.

"I'm certain we will find a mutually beneficial solution today," he said on arrival for what was set to be another marathon meeting.

Greece, where the euro zone's debt crisis erupted in late 2009, is the currency area's most heavily indebted country, despite a big "haircut" this year on privately-held bonds. Its economy has shrunk by nearly 25 percent in five years.

EU Economic and Monetary Affairs Olli Rehn said it was vital to disburse the next 31 billion euro tranche of aid "to end the uncertainty that is still hanging over Greece". He urged all sides to "go the last centimeter because we are so close to an agreement".

Negotiations have been stalled over how Greece's debt, forecast to peak at 190-200 percent of GDP in the coming two years, can be cut to a more sustainable 120 percent by 2020.

Without agreement on how to reduce the debt, the IMF has held up payments to Athens because there is no guarantee of when the need for emergency financing will end.

The key question is: Can Greek debt become sustainable without the euro zone writing off some of the loans to Athens?

IMF Managing Director Christine Lagarde said on arrival that the solution must be "credible for Greece".

A source familiar with IMF thinking said the global lender was demanding immediate measures to cut Greece's debt by 20 percentage points of GDP, with a commitment to do more to reduce the debt stock in a few years if Greece fulfills its program.

Under the source's scenario, Greece's debt could be reduced to around 125 percent of GDP by 2020 using a variety of methods including a debt buyback, reducing the interest rate on loans and returning euro zone central bank 'profits' to Greece, but further steps would still be needed to hit the 120 percent goal.

The ministers took an extended break in mid-afternoon while experts worked on how to formulate a link between short-term measures and a credible assurance of eventual debt relief.

Germany and its northern European allies have so far rejected any idea of forgiving official loans to Athens.

DEBT RELIEF "NOT ON TABLE"

German Finance Minister Wolfgang Schaeuble told reporters on arrival that a debt cut now was legally impossible, not just for Germany but for other euro zone countries, if it was linked to a new guarantee of loans.

"You cannot guarantee something if you're cutting debt at the same time," he said. That might not preclude debt relief at a later stage if Greece has completed its adjustment program and no longer needs new loans.

The source familiar with IMF thinking said a loan write-off once Greece has established a track record of compliance would be the simplest way to make its debt viable, but other methods such as foregoing interest payments, or lending at below market rates and extending maturities could all help.

The German banking association (BDB) said a fresh "haircut" or forced reduction in the value of Greek sovereign debt, must only happen as a last resort.

Two European Central Bank policymakers, vice-president Vitor Constancio and executive board member Joerg Asmussen, said debt forgiveness was not on the agenda for now.

Asmussen told Germany's Bild newspaper the package of measures would include a substantial reduction of interest rates on loans to Greece and a debt buy-back by Greece, funded by loans from a euro zone rescue fund.

So far, the options under consideration include reducing interest on already extended bilateral loans to Greece from the current 150 basis points above financing costs.

How much lower is not yet decided -- France and Italy would like to reduce the rate to 30 basis points (bps), while Germany and some other countries insist on a 90 bps margin.

Another option, which could cut Greek debt by almost 17 percent of GDP, is to defer interest payments on loans to Greece from the EFSF, a temporary bailout fund, by 10 years.

The European Central Bank could forego profits on its Greek bond portfolio, bought at a deep discount, cutting the debt pile by a further 4.6 percent by 2020, a document prepared for the ministers' talks last week showed.

Not all euro zone central banks are willing to forego their profits, however, the German Bundesbank among them.

Greece could also buy back its privately-held bonds on the market at a deep discount, with gains from the operation depending on the scope and price. Officials have spoken of a 10 billion euro buy-back at around 30 cents on the euro, that would retire around 30 billion euros of debt, although since the idea was raised the potential gain has fallen as prices have risen.

But the preparatory document from last week said that the 120 percent target could not be reached in 2020, only two years later, unless ministers accept losses on their loans to Athens, provide additional financing or force private creditors into selling Greek debt at a discount.

The latest analysis for the ministers showed the debt could come down to 125 percent of GDP in 2020, one euro zone official with insight into the talks said.

FORGIVING OFFICIAL LOANS?

German central bank governor Jens Weidmann has suggested that Greece could "earn" a reduction in debt it owes to euro zone governments in a few years if it diligently implements all the agreed reforms. The European Commission backs that view.

An opinion poll published on Monday showed Greece's anti-bailout SYRIZA party with a four-percent lead over the Conservatives who won election in June, adding to uncertainty over the future of reforms.

German paper Welt am Sonntag said on Sunday that euro zone ministers were considering a write-down of official loans for Greece from 2015, but gave no sources, and a euro zone official said such an option was never seriously discussed.

(Additional reporting by Robert-Jan Bartunek, Ethan Bilby, Luke Baker in Brussels, Reinhardt Becker in Berlin, Astrid Wendlandt in Paris; Writing by Jan Strupczewski and Paul Taylor; editing by Philippa Fletcher)