EU member states have agreed that around 100 billion euros is needed to recapitalize the European banking system, but splits remain before a high-profile summit on Sunday over how to strengthen the euro zone's bailout fund.

EU officials told Reuters all 27 member states were now agreed that just short of 100 billion euros ($138 billion) was required, while a banking source said the figure was more than 90 billion.

Banks will be required to come up with the capital from shareholders first, and if that fails than national governments will have to provide the support. Only as a last resort will the European Financial Stability Facility, the region's bailout fund, be used to recapitalize at-risk institutions.

The figure has been discussed with member states. It is now acceptable for everybody, an EU source involved with the discussions said. Austria's Finance Minister Maria Fekter said there was also discussion about forcing banks to recapitalize, although she said she was not in favor of such a move.

An agreement on bank capital needs clears one hurdle for European leaders ahead of Sunday's summit, but there remain large areas of disagreement, particularly over how to scale up the EFSF to make its lending more effective.

The International Monetary Fund and the EU also do not see eye-to-eye over the sustainability of Greece's debts, with the IMF concerned that EU projections may be too optimistic and that deeper debt reduction is needed, EU sources told Reuters.

An analysis by the European Commission, European Central Bank and the IMF on the debt sustainability will be presented to euro zone finance ministers on Friday, the European Commission said, playing down disagreement among the 'troika'.

Despite the difference of opinion, the inspectors are expected to go ahead and approve an 8 billion euro payment of aid to Greece next month, the sixth tranche from a 110 billion euro package of EU/IMF loans agreed last May.

Without that loan payment Greece faces default, possibly dragging the larger economies of Spain and Italy into the mire and sending shockwaves through the European banking system.

In their effort to agree a comprehensive crisis resolution plan on October 23, euro zone leaders are striving to agree new steps to reduce Greece's debt, strengthen the capital of banks with exposure to troubled euro zone states and leverage the EFSF to stem contagion to bigger economies.

But progress appears to be glacial, particularly when it comes to modifications to the EFSF, a 440 billion euro fund set up last year and so far used to bail out Portugal and Ireland.

Sarkozy flew to Frankfurt on Wednesday for emergency talks with German Chancellor Angela Merkel, the head of the IMF and other key euro zone officials. French media reported he missed the birth of his daughter in the process.

France has argued the most effective way of leveraging the EFSF is to turn it into a bank which could then use funding from the European Central Bank, but both the ECB and Berlin oppose this and the proposal now appears to be dead.

Instead, there is an initiative to use the EFSF to guarantee a portion of potential losses on new euro zone debt issuance, a way of trying to restore market confidence that the debts of Italy and Spain are to buy. By guaranteeing only a portion, perhaps a third or a fifth, of each debt issue, the EFSF's funds would stretch 3-5 times further.

Failure to reach a deal at Sunday's summit of European leaders would further undermine market confidence in the currency bloc and its ability to solve a two-year-long debt crisis, which threatens the viability of the single currency.

Markets caught up with the downbeat tone from policymakers. European shares fell having risen this week on hopes of comprehensive action from euro zone leaders.

Since France's finance minister pledged a decisive outcome to Sunday's summit last Saturday, expectations have been downplayed with Germany and others saying it will only be another step along the road to solving the debt crisis.

I don't think they can meet expectations. The summit will fall well, well short of the kind of big bang needed to reassure the markets, said Simon Tilford, chief economist at the Center for European Reform in London.

Canada's Finance Minister Jim Flaherty said Europe's two-steps-forward, one-step-back approach was disconcerting.

Showing its vulnerability, Spain paid high borrowing costs to sell 3.9 billion euros of bonds after a run of credit-rating downgrades.

Without more firepower, the EFSF will not have the means to defend Spain and Italy from market attack.

Guidelines for the bailout fund obtained by Reuters confirmed it will be able to buy bonds on the secondary market once a request from a country is approved by ECB and euro zone finance officials.

A draft statement for Sunday's summit showed euro zone countries will make rules to limit budget deficits and public debt part of national legislation by the end of next year.

But the statement gave no indication of progress on the main areas of dispute.

FORCED BANK LOSSES?

Adding to the uncertainty over whether a convincing deal can be struck on Sunday, EU officials said there was growing acceptance among key euro zone member states that further private sector involvement in Greece's debt reduction may have to be forced, not voluntary -- an outcome ruled out up to now.

Let's be serious, everybody knows that a 50 percent haircut, as Germany is asking for, is not a voluntary move, one EU official said.

In July, private sector investors agreed to contribute 50 billion euros to reducing Greece's debt via a debt buyback and swap agreement, which equated to a 21 percent writedown. That is now seen as insufficient to make Athens' debts sustainable.

Greece remains mired in recession and its overall debt is forecast to climb to 357 billion euros ($492 billion) this year, or 162 percent of annual economic output -- which few economists believe can be paid back.

When it comes to the EFSF, analysts are unconvinced that a leverage plan involving a guarantee on first losses would work without an explicit commitment from the ECB to go on buying at-risk debt, something it has been reluctant to do.

While Europe's leaders rush to stop a larger writedown of Greek debt infecting others in the euro zone, ordinary Greeks are raging at the prospect of years more pain as the price of help from international lenders.

Greek protesters marched on parliament, raising the prospect of more violence in strikes against austerity measures parliament is poised to approve to try to stave off bankruptcy.

Running battles between black-clad demonstrators and riot police on Wednesday left streets in central Athens covered with smoldering rubbish and lumps of masonry hacked off buildings. ($1 = 0.725 Euros)

(Additional reporting by Gernot Heller and Madeline Chambers in Berlin, Andreas Rinke and Luke Baker in Brussels and Michael Shields in Vienna; Writing by Mike Peacock; editing by Janet McBride)