By Silvia Aloisi and Paola ArosioMILAN (Reuters) - Italy has dubbed its new bank bailout fund Atlas, after the mythical Greek titan, because it is meant to hold up the sky above the nation's lenders. But some of the fund's own investors doubt that it can do the job.The 5-6 billion euro ($5.7-6.8 billion) fund was hailed by the government as an industry-led response to concerns in Rome and other European capitals about the euro zone's fourth-biggest banking system.But it was only reluctantly accepted by some of the financial institutions that committed to it, according to seven sources, including four of the institutions that eventually agreed to put money in the fund.Some bankers involved in the scheme voiced fears the fund would expose their own banks to the self-inflicted problems of a few lenders, the sources said.They also said that the fund may not be big enough to make a real dent in Italy's 360 billion euros in bad debts, a third of the euro zone's total, if it spends most of its money on helping recapitalize weaker banks, according to the sources.Italy's biggest retail bank, Intesa Sanpaolo , and another lender, Banco Popolare , spoke out against Atlas in tense, closed-door meetings leading up to the fund's announcement on Monday, according to two sources who were present.Some bankers complained they were being asked to sign up to a multi-billion-euro fund without any documentation, the sources said.A person who played a key role in setting up the fund said some of the details were only fine-tuned at midday on Monday, so no paperwork was distributed at the final meeting with bankers in the evening. The plan's first formal draft circulated the following day.Unenthusiastic bankers only agreed to back it after government and central bank officials warned of a crisis of confidence in the sector unless big lenders signed up.The person who had a key role in setting up the fund said they were told that if a single bank's effort to raise cash on the market failed, it would drag the whole industry down.Intesa Sanpaolo and Banco Popolare declined to comment on the talks leading up to the fund's creation and on whether they had reservations about the scheme.A Bank of Italy spokeswoman said it supported the initiative by private financial institutions, which the central bank governor has described as a safety net to ensure choppy markets do not impede the necessary recapitalization of some lenders."The backstop offered by Atlas will have positive effects on the problem of non-performing loans, which is the main problem of Italian banks," the spokeswoman said.The government did not respond to emails requesting comment on whether some banks had doubts about the plan, and whether it had exerted any pressure on institutions to participate.The initial reluctance of big players to invest in Atlas casts uncertainty over the long-term future of a fund meant to shore up Italian banks, which fared the worst in Europe-wide stress tests of their financial resilience and have lost a third of their value this year due to concerns over their bad debts.However, other financial institutions expressed support for the scheme, which has around 40 institutional investors, including insurers, banking foundations and state lender Cassa Depositi e Prestiti, saying something needed to be done."It is a positive initiative for the system," said Banca Popolare di Milano Chief Executive Giuseppe Castagna, adding he hoped only a small part of the fund's cash would be needed to assist cash calls at weaker banks. "We hope the announcement itself will soothe the market, so that a bigger portion of the fund can be used for bad debts."Ennio Doris, chairman of asset manager Mediolanum which is contributing 50 million euros, told Reuters the scheme was aimed at making the banking industry more solid.DISTRESSEDThe fragility of Italy's banking system has increasingly been a factor in a debt crisis that has haunted the euro zone since 2009. Any further risks to its stability could hinder both the Italian and regional economic recoveries.The sector has long suffered from low profitability, weak governance and high costs. A severe recession added to the problems by making many companies default on loans, saddling banks with soured debts that - if they are written down at their market value - would blow a capital hole in their accounts.If the bailout fund runs out of money, initial participants would be asked to contribute more cash, but are not obliged to do so. A person with direct knowledge of the matter said he expected banks that put in money now to be willing to increase the fund's fire-power at a later stage if needed, but that if this was not the case other players may join the scheme.Rating agencies Fitch and Standard & Poor's expressed concern the fund was chipping away at stronger banks to prop up the ailing ones."We believe that banks investing in the vehicle could be asked to increase their participation in the future and, thus, their exposure toward weaker financial institutions," S&P said.Atlas will use most of its cash to buy shares in stock issues at distressed banks, with the rest earmarked to buy bad loans, focusing on junior debt where investor demand is weakest.To help the fund, the government has pledged to speed up bankruptcy procedures. It takes eight years to recover overdue loans in Italy, four times longer than the European average, which makes them unattractive for distressed-debt investors.RIGHTS ISSUESNo detailed plans have been announced. But the fund may have to invest up to 2 billion euros in two smaller banks' rights issues, including an imminent share sale by Banca Popolare di Vicenza, the source with direct knowledge of the issue said.Intesa Sanpaolo Chief Executive Carlo Messina had flatly rejected the idea of Atlas in a preliminary meeting at the end of March, two of the sources said. He agreed in subsequent meetings to put 1 billion euros into the scheme only after receiving assurances that the fund would not spend all its money on buying shares in faltering banks, they said.Messina said on Wednesday the fund would help banks sell bad debts close to book value and not at the heavily discounted prices demanded by "loan-shark" private equity funds. This, coupled with the government plan to quicken bad loan recovery, will improve the context in which banks operate, he said.Banco Popolare Chief Executive Pier Francesco Saviotti had also initially criticized the plan, saying it would benefit big rival UniCredit , which is heavily exposed to Popolare di Vicenza.He was voicing reservations right up until the final meeting on Monday that he could not understand why the whole financial industry should mop up shares of ailing banks when his own lender planned, unaided, to raise 1 billion euros in the next few months, said one of the sources.Other banks shared Saviotti's doubts."The most frequently asked question was: are we here to throw a lifeline to UniCredit'" said one source who was briefed about the discussions.UniCredit is currently the sole guarantor of Popolare di Vicenza's 1.76-billion euro cash call, meaning it would have to take on any unsold shares in the rights issue if investor demand remains weak, putting its own capital ratios at risk.UniCredit, which is contributing 1 billion euros to the fund, declined to comment on the meetings. Its chief executive, Federico Ghizzoni, said on Thursday the vehicle was not set up to bail out Popolare di Vicenza. "We did not seek Atlas's help, it's the other way round," he said.Mediobanca , Italy's top investment bank, did not attend Monday's meetings, having decided to snub the scheme, three sources said. Mediobanca declined to comment."Maybe it's not perfect but at least it's something," said the chief executive of a mid-tier bank investing in Atlas who declined to be named due to the confidential nature of the talks. "Would it be better to do nothing at all'"(Additional reporting by Andrea Mandala, Gianluca Semeraro and Maria Pia Quaglia in Milan, and Stefano Bernabei in Rome; Editing by Mark Bendeich and Pravin Char)Join the conversation about this story Click here to read full news..