Greece and its private creditors head back to the negotiating table on Saturday to put together the final pieces of a long-awaited debt swap agreement needed to avert an unruly default.

After weeks of muddling through round after round of inconclusive talks, the negotiations appear to be in their final phase, with both sides hoping to secure a preliminary deal before Monday's European Union summit.

Prime Minister Lucas Papademos was expected to meet bankers' chief negotiator Charles Dallara at around 1330 GMT (8:30 a.m. EST) on Saturday, before meeting inspectors from the troika of foreign lenders pressing Athens to step up painful reforms.

Today will be another tough day, said George Karatzaferis, leader of the far-right LAOS party, one of three parties in Papademos's emergency coalition government. We will see whether we can bear the burden that lies ahead.

The debt swap, in which private creditors are to take a 50 percent cut in the nominal value of their Greek bond holdings in exchange for cash and new bonds, is a prerequisite for the country to secure a 130-billion-euro rescue package.

Papademos told Reuters in an interview on Friday he expected the debt talks to be concluded within days.

We made significant progress over the last few weeks and in the last few days in particular. We are trying to conclude the discussions as quickly as possible. I am quite optimistic an agreement will be reached in the coming days, he said.

But concern has grown that the deal may not do enough to get the country's debt reduction plan back on track, and that Greece's European partners will be forced to stump up funds to cover the shortfall.

The German news magazine Der Spiegel reported on Saturday that Greece's international lenders thought Athens would need 145 billion euros of public money from the euro zone for its second bailout rather than the planned 130 billion euros.

The magazine said the extra money was needed because of the deteriorating economic situation in Greece, echoing a Reuters report on Thursday.

Athens also faces problematic talks with the troika of foreign lenders - the European Commission, IMF and European Central Bank - who have warned it needs to do more to drive through painful reforms before they dole out any more money.

It's all very dense, difficult and crucial, a Greek finance ministry official said. There is optimism because the country needs to survive and we need to protect its citizens because they have suffered a lot.

Athens and its creditors have broadly agreed that new bonds under the swap would probably have a 30-year maturity and a progressive interest rate. The deal is aimed at chopping 100 billion euros off Greece's crushing 350-billion-euro debt load.

But they have wrangled for weeks over the interest rate Greece must pay on the new bonds and pressure has grown in recent days on the European Central Bank and other public creditors to accept a cut in the value of their Greek bond holdings like the private sector creditors.

A debt deal must be sealed in about three weeks as Greece has to repay 14.5 billion euros of debt on March 20. Otherwise Greece will sink into an uncontrolled default that might spread turmoil across the euro zone.

Papademos promised on Friday this would not happen. Greece will not default, he said.

International Monetary Fund Managing Director Christine Lagarde said on Saturday that euro zone members were making progress to overcome their crisis but must do more to strengthen their financial firewall, adding that the IMF was ready to help.

There is progress as we see it, Lagarde told a panel discussion at the World Economic Forum in Davos.

But it is critical that the euro zone members actually develop a clear, simple, firewall that can operate both to limit the contagion and to provide this sort of act of trust in the euro zone so that the financing needs of that zone can actually be met.

Senior euro zone officials have expressed optimism on the Greek debt deal, though previous predictions of an imminent agreement have failed to become reality.

Greece is in its fifth year of recession, and hopes of an end to the crisis in the near term have virtually gone, because of the combination of squabbling politicians, rising social anger and its inability to get its debt load under control.

Germany is pushing for Greece to relinquish control over its budget policy to European institutions as part of discussions over a second rescue package, a European source told Reuters on Friday.

Greece said such a move was out of the question, adding that a similar proposal had been made in the past by a Dutch minister without getting anywhere.

There is no way we would accept such a thing, a Greek government official told Reuters.

(Additional reporting by Renee Maltezou, Writing by Deepa Babington; editing by Tim Pearce)