(REUTERS) -- Greece's tortuous negotiations over a debt swap with private creditors entered a new phase on Thursday with focus on how much the European Central Bank and other public creditors may need to contribute.

Athens, which needs a deal quickly to avert a chaotic default when a major bond redemption comes due in March, hopes the talks can be wrapped up this week.

The top negotiator for the banks and insurers, Charles Dallara, is scheduled to meet Prime Minister Lucas Papademos in the early evening after experts meet to discuss technical details.

International Monetary Fund Managing Director Christine Lagarde put pressure on the ECB on Wednesday, saying it and other public creditors may need to accept losses if those taken by the private sector are not enough to bring Greece's debt burden down to a sustainable level.

The European Union's top economic official also said more public money will be needed to make up a shortfall in a second bailout for Greece after a debt swap deal is clinched in the coming days.

We are preparing a package which will pave the way for a sustainable solution for Greece, and in that package, yes, on the basis of the revised debt sustainability analysis, there is likely to be some increased need of official sector funding, but not anything dramatic, EU Economic and Monetary Affairs Commissioner Olli Rehn told Reuters.

Private bondholders want others who bought bonds, and in particular the ECB which is Athens' single biggest creditor, to take part in a swap deal where existing bonds are exchanged for new paper offering far lower returns.

We are ready to make an effort if everyone else (including the ECB) makes an effort, a source close to the talks said.

The interest rate, or coupon, on the new bonds has been the main stumbling block in the negotiations, with the IMF, Germany and other euro zone countries insisting it must be low enough to ensure that Greece's debt will fall to a still mighty 120 percent of GDP by 2020, from around 160 now.

One source familiar with the negotiations said the coupon is parked for current time until we can get closer on detail of the overall package. Asked if that would include the ECB, the source said: We would expect it to, still to be determined though.

A second source close to the talks said the latest a deal could be clinched is a month before 14.5 billion euros of bond redemptions fall due on March 20, i.e., in just over three weeks.

If a deal is not reached by then, Greece could sink into an uncontrolled default that would trigger a banking crisis spreading contagion through the euro zone.

The ECB's creation of nearly half a trillion euros of three-year money for the banks in December has tempered that fear.

High debtor Italy saw its government bond yields and the cost of insuring against a default fall on Thursday, helped by solid demand for short-term debt at an auction.

ECB ROLE?

Greek bankers and government officials said they had not heard of any new proposal from the creditors' negotiators, after local media reported they were willing to improve their final offer of a 4 percent interest rate on the new bonds to about 3.75 percent.

One Greek daily, Kerdos, said participation of public sector creditors including the ECB in the swap deal was a pre-condition for that offer.

Until last week, we knew that the steering committee was authorized to concede up to 3.8 percent for the average coupon, one senior Greek banker told Reuters.

But things are once again up in the air. You have to deal with politicians and 15 different governments asking for different things. We haven't got anything clear from the IIF yet, discussions start today.

Euro zone ministers rejected on Monday the creditors' offer of a 4 percent coupon on new bonds, increasing the chance that Athens would have to enforce losses. Greece and its EU/IMF lenders were holding out for a 3.5 percent interest rate.

Euro zone finance ministers wanted a coupon capped at 3.5 percent for the initial period to 2020 and then capped at 4 percent until 2030, the second source close to the talks said, adding: If this is the deal, we'll take it.

The source also confirmed that ECB was likely to be included in the debt swap talks.

The ECB had ruled out taking voluntary losses on its Greek bond holdings but is now debating how it would handle any forced losses and whether to explore legal options to avoid such a hit, central bank sources told Reuters on Wednesday.

The Institute of International Finance, which Dallara heads, said Thursday's discussions would be informal and aim to sort out legal and technical issues quickly. Dallara left Athens over the weekend after the last round of talks proved inconclusive.

Senior EU, IMF and ECB officials are holding talks with the Greek government in parallel with the debt swap talks, to flesh out a new 130-billion euro bailout for Greece. They have warned they need the debt swap to cut Greece's debt substantially in order to go ahead with the new loans.

Germany does not expect the troika of foreign lenders to deliver a report on Greece's progress before a summit of European Union leaders on Monday, a senior German official said on Thursday, adding that this meant that Greece would not play a major role at the EU leaders summit.

Greece has made little progress on reforms as it stumbles through its worst post-World War II economic crisis. The task facing the country has been made harder with anger against austerity measures and squabbling politicians running high.

A poll on Thursday showed Greece's conservatives had widened their lead over socialist coalition partners ahead of elections expected in April, but they would not win an absolute majority if elections were held now.

(Additional reporting by Sarah White and Sophie Sassard in London, Paul Taylor and Axel Threlfall in Davos, Harry Papachristou and Tatiana Fragou in Athens,; Writing by Deepa Babington. Editing by Jeremy Gaunt.)