UPDATE 1-Italy working with EU authorities to find solution for Veneto banks

* Popolare Vicenza, Veneto Banca have requested state aid

* EU demands 1 bln euro contribution to clear state bailout

* "Bail in" fears hit lenders' senior bonds (Combines stories, adds details)

MILAN, May 25 (Reuters) - Italy is working with European authorities to find a rapid solution for troubled regional banks Popolare di Vicenza and Veneto Banca, the government said, as investors worried that the lenders may fail to get the state aid they have requested.

Italy has been in talks with Brussels for months over its plans to rescue the two banks based in the northeastern Veneto region and bigger rival Monte dei Paschi di Siena under strict European Union rules that curb state support for lenders to shield taxpayers.

Rome is reluctant to wind them down to avoid knock-on effects on other banks, which have emerged weakened from a long recession that sent bad loan levels soaring.

"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 in a statement on Thursday, issued after a meeting between Economy Minister Pier Carlo Padoan and the two bank's top managers.

"The government is committed to finding a solution quickly," it said, adding that a meeting in Brussels on Wednesday had been only one of several technical steps needed to assess the bailout request.

Sources have said that on Wednesday EU authorities stood by their demand for a 1 billion euro ($1.1 billion) private capital contribution to the rescue, rejecting Italian requests for smaller involvement by private investors.

Highlighting how difficult finding fresh capital would be, the head of Italy's biggest retail lender Intesa Sanpaolo said on Wednesday that healthy banks in the country should not be forced to spend more money rescuing weaker rivals.

Italy's leading banks and insurers have already pumped 4.4 billion euros into the two Veneto lenders through the state-sponsored bailout fund Atlante. It took them over a year ago but is now unwilling to 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 to approve the rescue 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.

Unlike Spain or Ireland, Italy failed to help its banks before strict 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.

A Milan-based trader said that Popolare di Vicenza and Veneto Banca had at least three bonds totalling 1.45 billion euros that were mostly held by institutional investors. ($1 = 0.8912 euros) (Reporting by Valentina Za; editing by Francesca Landini and David Stamp)