* Italy has done what is needed to save itself -industry minister

* Govt always worried about avoiding "abyss" -cooperation minister

* Govt less worried than it was when Monti took over -minister (Adds quotes from Passera, cooperation minister, background)

MILAN, June 11 (Reuters) - Measures adopted by Italy so far have put the euro zone's third-largest economy on a sound footing to face the current financial turmoil, the country's industry minister said on Monday, dismissing the idea Rome may need external help.

"Italy has done what was necessary to save itself in past months," Industry Minister Corrado Passera said when asked if Spain's aid deal meant that a bailout for Italy was likely.

Speaking on the margins of a conference in Milan, Passera told reporters that austerity measures adopted so far have put Italy "among the countries better placed to deal with the financial turmoil Europe finds itself in."

After the weekend deal in which euro zone leaders agreed to lend Spain up to 100 billion euros to recapitalise its debt-laden banks, many analysts believe Italy may be the next country to seek assistance.

A European market rally early on Monday fizzled out quickly. Italian benchmark bond yields rose above 6 percent at one point, less than half a point below Spain's levels. The spread compared with safer German Bunds rose to around 4.6 points, compared with a recent low of 2.8 points in March.

Andrea Riccardi, minister for International Cooperation, sounded slightly less upbeat than Passera when asked if the government was more worried about the crisis spreading to Italy following the bailout for Spain's banks.

"This government has always been worried, our commitment has always been accompanied by our concern to avoid the abyss," he told Reuters. "Today we are watching what is happening in Spain very closely, but we are much less worried than we were in November" when Prime Minister Mario Monti took office.

Monti formed a government of technocrats when a discredited Silvio Berlusconi stepped down in November as Italy seemed headed toward a Greek-style default on its massive debt.

To shore up investor confidence, Monti immediately passed a tough austerity package, including new taxes and pension cuts, which is now weighing on his popularity.

Italy is facing headwinds both from the broader euro zone debt crisis and the growing domestic difficulties for Monti, who admitted last week that he had lost the support of important parts of the country's establishment.

He was referring in particular to a front page editorial in Italy's most influential daily, Corriere della Sera, in which two prominent economists, Francesco Giavazzi and Alberto Alesina, said Monti's early reform drive had petered out and its policies now seemed very similar to its predecessors'.

The economy is mired in a deep recession which shows no sign of easing and parts of the ruling majority are openly discussing whether it would be better to pull support from Monti and hold an early election before the end of this year.

"We must all save ourselves together (because) no-one can save themselves alone," Passera said in support of the deal for Spain.

"The cost of not saving Europe and allowing the euro to disintegrate, which can absolutely be avoided, would be higher than the cost of helping the countries in difficulty to make the necessary adjustments." (Reporting by Elvira Pollina and Steve Scherer, writing by Gavin Jones. Editing by Jeremy Gaunt.)