* FITD depositor protection fund considers new rescue plan
* Plan involves bank's shareholders, private/public investors
* Apollo submitted new offer after initial proposal rejected (Recasts with details)
By Stefano Bernabei
ROME, June 25 (Reuters) - A rescue plan for ailing Italian Carige funded by rival lenders alongside public and private investors will involve a larger-than-planned capital injection of around 800 million euros, a source with knowledge of the matter said.
Carige, weakened by mismanagement and bad loans, was placed under special administration by the European Central Bank on Jan.2 after failing to push through a 400 million euro ($455 million) fundraising.
The bank's administrators in February unveiled a 630 million euro capital shortfall and embarked on finding a buyer for the Genoa-based bank.
But rescue efforts faltered after U.S fund BlackRock last month dropped a possible bid for Carige. The administrators on Monday received an improved offer from Apollo after an earlier proposal by the U.S. private equity firm was rejected.
In the meantime, a depositor protection fund financed by Italian banks is studying a rescue plan that involve Carige's shareholders as well as private and public investors.
The fund, known as the FITD, had already propped up Carige in November by buying a 320 million euro hybrid bond that Carige had been unable to sell on the market to boost its capital.
Two sources close to the matter said that bond would be converted into equity as part of the FITD's rescue, effectively turning Italian banks into Carige shareholders.
One of the two sources said the bond would cover less than half of Carige's capital needs which have increased to around 800 million euros.
The Italian media reported on Tuesday that the government could step in to provide 100-200 million euros through an agency controlled by the Treasury. The Treasury had no immediate comment.
The bank's biggest shareholder, the Malacalza family of steel billionaires, is also considering whether to invest further in the bank to avoid seeing its 27 percent stake diluted.
The Italian government in January provided emergency liquidity to Carige by guaranteeing 2 billion euros in bond issues. It has also set aside 1.3 billion euros to buy the bank's shares by the end of September.
A state rescue is an unpalatable option for the ruling coalition made up of the right-wing League and anti-establishment 5 Star Movement which have lashed out at the previous centre-left government over bank bailouts.
Carige's problems are common among a lot of Italian regional banks, which for decades were closely entwined with local interests and were hit hard by a recession that wiped out a quarter of the country's industrial output.
$1 = 0.8787 euros Additional reporting by Giuseppe Fonte, writing by Valentina Za. Editing by Giselda Vagnoni and Jane Merriman