* Popolare di Vicenza, Veneto Banca have requested state aid
* EU demands 1 bln euro contribution to clear state bailout
* "Bail in" fears hit lenders' senior bonds (Adds Atlante option, Viola report)
By Giuseppe Fonte and Valentina Za
ROME/MILAN, May 25 (Reuters) - Italy's economy minister sought to reassure investors on Thursday that they will not be hit in a rescue of two ailing regional banks, Popolare di Vicenza and Veneto Banca, after fears of a full "bail-in" hit the lenders' debt.
Italy has been seeking European Union approval for months to rescue the two banks based in the northeastern Veneto region and bigger rival Monte dei Paschi di Siena under strict EU rules that curb state support for lenders.
Under such rules, which aim to shield taxpayers from the full cost of saving failing banks, private investors - shareholders, senior bondholders and large depositors - must bear losses before any public money can be used, in what has become known as a "bail-in".
Italy is keen to avoid such a scenario, fearing this would hurt confidence in the wider banking sector, already weakened by a long recession that sent bad loan levels soaring.
Rome wants to exploit an exception to the rules and inject money into the lenders under a precautionary recapitalisation scheme that spares losses to senior bondholders and depositors.
"I rule out the possibility of a 'bail-in'," Economy Minister Pier Carlo Padoan told reporters when asked about negotiations with EU authorities over the rescue.
There is no easy solution for the two banks, which have been told by the European Commission to secure an additional private capital injection of 1 billion euros before a state bailout can be approved, several sources in banking and government said.
With willing investors in short supply, the Italian government is putting pressure on healthier banks to provide the funds, the sources told Reuters.
One option would be to use Atlante, a government-sponsored fund financed by Italian banks and insurers set up last year to rescue the Veneto banks after they failed to raise money on the market, two banking sources said on Thursday.
Atlante has already pumped 3.4 billion euros into the two lenders. It has 1.7 billion euros left, earmarked to help Monte dei Paschi and other banks offload their bad loans. The fund, which other sources say is unwilling to put more money in the two lenders, declined to comment.
Highlighting how hard finding fresh money would be, the head of Italy's biggest retail lender Intesa Sanpaolo said on Wednesday that strong banks in the country should not be forced to spend more money rescuing weaker rivals.
In another sign of the seriousness of the situation, a source with knowledge of the matter said Popolare di Vicenza CEO Fabrizio Viola, who is leading the talks with European regulators on behalf of both lenders, has not ruled out quitting his job.
Padoan met top executives from the two banks early on Thursday after a meeting in Brussels on Wednesday when, according to sources, EU authorities stood by their demand for additional private capital.
The money would help fill a 6.4 billion euro capital shortfall identified by the European Central Bank.
Fears that senior bondholders may be forced to contribute to the private capital needed hit senior bonds issued by Popolare di Vicenza and Veneto Banca on Thursday.
Under the current rescue plan, only junior bondholders stand to take a hit.
In a statement published on Thursday, the economy ministry played down Wednesday's meeting in Brussels, saying it was only one of several technical steps needed to assess the bailout request.
"Talks with European authorities continue with a shared goal of agreeing a solution that guarantees the stability of the two Veneto-based banks and fully preserves savers, in compliance with European rules," the Treasury said. "The government is committed to finding a solution quickly."
The two banks said they had called emergency board meetings for Friday.
Unlike Spain or Ireland, Italy failed to help its banks before the new EU rules over bank crises came fully into force last year. It now has little room to support its lenders without hurting small savers that hold much its banks' debt and shares.
In past months, depositors have fled weaker Italian banks, fearing they might have to participate in a bail-in.
Monte dei Paschi, Popolare di Vicenza and Veneto Banca have all been forced to tap a state guarantee to be able to issue debt and make up for the deposit flights.
"As far as liquidity is concerned, Banca Popolare di Vicenza and Veneto Banca have all the necessary state guarantees," the Treasury said.
$1 = 0.8912 euros additional reporting by Stefano Bernabei in Rome, editing by David Stamp and Sonya Hepinstall