MILAN (Reuters) - Italy's two biggest banks UniCredit (>> UniCredit SpA) and Intesa Sanpaolo (>> Intesa Sanpaolo SpA) plan to put 1 billion euros each into a fund to shore up the country's banking sector, a move that put pressure on their shares on Tuesday.

The state-backed fund is aiming to reach a total of 5 to 6 billion euros, according to a source with direct knowledge of the matter, and is designed to help weaker banks in the euro zone's fourth-largest banking sector.

Italy's banks are struggling with 360 billion euros ($409.75 billion) in bad loans, a third of the euro zone total, but bank analysts say the government-orchestrated fund is barely enough to cover the capital needs of a few struggling small lenders. "The problem with the Italian bank fund is that it is not big enough and it risks compromising the banks that are already in a much better shape," Francois Savary, chief investment officer at Geneva-based Prime Partners, said. Analysts say the fund's initial resources would be dwarfed by the potential capital needs of the bank with most bad loans relative to its loan book - Monte dei Paschi di Siena (>> Banca Monte dei Paschi di Siena SpA). The fund will also only have limited ability to borrow to scale up the size of its investments, two sources familiar with the matter said. Its mandate is to buy up bad loans from ailing banks and to underwrite their share issues.

The contributions from Intesa Sanpaolo, the country's strongest bank, and UniCredit would give them an outsized exposure to what some investors regard as an investment that could weigh on them and may not be profitable in the short term.

UniCredit declined to comment.

An announcement about the fund on Monday followed weeks of meetings between the government, Italy's central bank and financial institutions including state lender Cassa Depositi e Prestiti, which will contribute 500 million euros.

Rome wants to present the fund as primarily an industry initiative to avoid infringing European state aid rules. It has been named "Atlante" - Italian for the Greek god Atlas who carried the heavens on his shoulders.

Under the current plan, the fund would last for five years with an option to extend it for three more, the source said.

Draft documents on the scheme were distributed on Tuesday to the various institutions that have pledged to contribute to the fund, the source said. They are expected to call board meetings in the next few days to approve the amounts for the fund.

It aims to collect contributions by April 28, it added.

FUND'S FIRST TASK

Analysts say the big banks' willingness to put money in the fund reflects a desire to avoid a bank collapse that could trigger a run on deposits.

The source said smaller banks would stump up between 500 and 700 million euros, banking foundations around 520 million euros and insurers a further 500 to 700 million euros.

The plan is to use 70 percent of the fund's money to buy into cash calls to plug capital gaps at ailing banks, and use the rest to help banks to get rid of bad loans, the source said.

The fund may need to invest 2 billion euros in rights issues at Banca Popolare di Vicenza and Veneto Banca if there are a lot of unsold shares, and may end up taking control of at least one of the lenders, the source said.

Talks to set up the fund took on an added urgency in view of Banca Popolare di Vicenza's 1.76 billion euro cash call, which needs to be completed by May 10.

The bank has started sounding out investors, but sources say it has attracted little demand, possibly spelling trouble for UniCredit, which is currently the deal's sole guarantor.

($1 = 0.8786 euros)

(Writing by Isla Binnie and Silvia Aloisi; Editing by Jane Merriman and Alexander Smith)

By Silvia Aloisi