* Incomplete EU integration process creates vulnerabilities

* Italian banks must cut costs including through layoffs

* Italy’s public debt may not fall this year (Adds comments on vulnerabilities)

MILAN, May 31 (Reuters) - Bank of Italy Governor Ignazio Visco urged the European Union to backtrack on new rules aimed at shielding taxpayers from having to prop up ailing banks, warning authorities may be unable to stop contagion in a crisis.

Italy had a taste of tougher new EU rules on state aid when it rescued four small lenders from bankruptcy in November, wiping out the savings of hundreds of ordinary Italians who had bought the banks’ shares and junior bonds.

This hurt confidence and triggered an outflow of deposits at other weak banks when “bail-in” rules were fully introduced in January.

Visco, who has repeatedly called for bail-in rules to be revised, said the possibility of using public money in bank crises had been “virtually eliminated” while Europe-wide tools to deal with problems were not yet fully in place.

“This, in short, creates a situation of vulnerability. There is the danger not only that national and European authorities will be unable to react adequately to major shocks, but even that they will have trouble avoiding contagion,” Visco said.

To avoid a repeat of costly bank bailouts seen during the financial crisis, public money can now be tapped to help lenders only after investors and large depositors bear losses.

But Visco said prompt public intervention could prevent the destruction of wealth without necessarily generating losses for the state, and could even generate profits.

“Greater scope for intervention of this sort, exceptional as it may be, should be reinstated,” he said in a speech to the Bank of Italy’s annual assembly in Rome.

He criticised the EU Commission for blocking Italy’s plan to use a deposit guarantee fund financed by lenders to save the four small banks without hitting retail investors.

“There is no reason to stigmatize as improper state aid those initiatives that help to correct market failures without undermining competition,” he said.

“A rigid interpretation of the regulations on state aid, with little regard for financial stability, has also hindered the plan for creating a company to manage Italian banks’ non-performing loans.”

Unlike Spain or Ireland, Italy did not move to help its banks during the financial crisis, partly due to a public debt burden running at more than 1.3 times its output.

But when a three-year recession saddled Italian banks with 360 billion euros in soured debts, the government found itself with little room for manoeuvre.

Visco urged banks to swiftly cut costs, including through layoffs, to prop up profits after booking more than 120 billion euros in loan writedowns over the past four years.

“For many Italian banks it remains imperative to take steps to contain costs, including staff costs, by adapting the quality and quantity of personnel to new technological and market developments,” Visco said.

For smaller banks problems could be “acute” making rapid consolidation necessary.

Turning to public finances, Visco also warned that Italy’s public debt - the highest in the euro zone as a proportion of national output after Greece’s - may not come down this year as the government has targeted. (Additional reporting by Gavin Jones in Rome; Editing by Alexandra Hudson)