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Italy's financial industry has approved a government-backed plan to set up a rescue fund to help weaker banks.

The Atlante fund will be made up by private money, reportedly worth €5bn ($5.7bn; £4bn), and will buy up shares and bad debt in struggling banks.

Italy's banking industry is saddled with some €360bn of bad debt, around a third of the eurozone's total.

Investor concern over the strength of the industry has hit banking shares this year.

However, they soared on Monday in anticipation of the news.

Monte dei Paschi di Siene and Banco Popolare - two banks with the worst loan books - both saw their stock rise more than 10%.

The announcement of the fund came from the private fund manager Quaestio Capital Management.

"Following meetings with a vast number of institutional investors, banks, insurers, banking foundations and [state lender] Cassa Depositi e Prestiti, Quaestio has gathered many subscribers to launch the Atlante Fund," the fund manager said.

It did not detail the exact size but earlier the chief executive of Banca Popolare, Alessandro Vandelli, said it was worth about €5bn.

Prime Minister Matteo Renzi welcomed the agreement and said that the government would pass measures to make it easier to recover loans and speed up bankruptcy procedures.