* Intesa wants just healthy parts of Veneto lenders

* Clean-up costs could be dumped on state

* Rome criticised for bending rules on bank bailouts

By John O'Donnell and Silvia Aloisi

FRANKFURT/MILAN, June 22 (Reuters) - A clumsy attempt by Italy to tackle problems at two Veneto-based banks by allowing a major lender to cherry-pick their prime assets for a pittance has left the government testing the boundaries of European law.

With a deal expected within days, critics are concerned that Rome is exploiting loopholes to bend EU rules designed to prevent state bailouts.

One European official privately admitted to "exasperation", after the European Central Bank and European Commission have tussled with Rome for years over how to solve its banks' problems within EU law.

On Wednesday, Italy's biggest retail bank Intesa Sanpaolo laid down tough conditions to buy the healthy parts of the two Veneto banks for just 1 euro, a move that would force the state to foot the bulk of the bill.

Intesa said it would only take the banks if they were stripped of bad loans and risks, prompting criticism from those who designed the EU regime to stop the state from having to shoulder losses in bank crises, passing them on to investors instead.

That solution also contrasts starkly with Santander's recent overnight rescue of a struggling lender in Spain, where it too paid just 1 euro but took on the smaller bank's troubled loans and will raise billions to clean it up.

Rome is taking advantage of a flexibility in European rules that permits routine insolvency proceedings for banks not considered systemically important, allowing the process to be handled by the state rather than EU authorities.

One EU official said state aid in this case might be technically possible given that banks' shareholders and junior bondholders are also going to take a hit.

But critics said Italy was being allowed to cut corners.

"The Italians do not respect the rules. The ECB and the Commission are too weak to enforce them," said Sven Giegold, a German member of the European Parliament. "This is destroying trust."

Italy is the last country in the euro zone to get to grips with the problems of its banking sector, meaning it faces stricter 'bail-in' rules - written by Giegold and others and introduced last year - that impose losses chiefly on bondholders and investors.

With elections due next year and much of its banks' debt in the hands of ordinary Italians, Rome wants to avoid this step.

"The signals from Italy are very negative," said Volker Wieland, one of the German government's economic advisors.

Wieland accused Italy of "looking for exceptions" to the rules, warning that such an approach would discourage Germany from supporting any common European protection of deposits, a proposal made to underpin confidence in the region's lenders.

The ECB, which supervises Italian banks, and the EU Commission, which rules on whether state support can be allowed, have declined to comment on the Italian proposal, saying they await a formal announcement from Rome.

NO HIDING PLACE

At home too the tactics in Rome - after more than six years of procrastination through the country's banking crisis - are raising questions.

The government had hoped healthier Italian banks would club together to help the lenders, Banca Popolare di Vicenza and Veneto Banca.

But most demurred, having already spent billions propping up ailing banks, including through the government-sponsored Atlante fund that pumped 3.4 billion euros into the Veneto banks and is now set to be wiped out.

Others had problems of their own, such as Monte dei Paschi, which is being bailed out by the state using another exception to the EU rules. Most banks said the government should stop asking them to chip in, and use instead the 20 billion euros it set aside for bank rescues, negotiating terms with Brussels.

Opposition politicians have been critical.

"Intesa gets a free gift, the state takes on all the bad stuff and the taxpayer pays," said Renato Brunetta, parliamentary leader for former prime minister Silvio Berlusconi's Forza Italia (Go Italy!) party, estimating the cost for the Italian state could be 5-6 billion euros.

"Did we really need to take so much time to come up with such a rubbish solution?"

Carla Ruocco, a prominent lawmaker of the 5-Star movement, echoed this view: "By wasting years, the government put itself in a bind." (Additional reporting by Gavin Jones in Rome and Francesco Guarascio in Brussels; writing by John O'Donnell; editing by John Stonestreet)