By Stefano Bernabei

SIENA, Italy (Reuters) - Shareholders in Monte dei Paschi di Siena <BMPS.MI> approved a 5 billion euro ($5.3 billion) share issue on Thursday, the third cash call in as many years to keep Italy's third-biggest lender afloat.

The Tuscan bank, the world's oldest still in business, needs to raise more than seven times its market value in cash in order to sell bad loans and boost capital after industry stress tests in July singled it out as Europe's weakest.

New Chief Executive Marco Morelli told shareholders he had showcased the bank's rescue plan to more than 250 investors, including hedge funds and sovereign wealth funds, in the 70 days since taking office, but had failed to obtain any firm backing.

Weighing on investors' mind is a constitutional referendum on Dec. 4 which could topple Italy's reformist government and usher in a period of political instability.

The Monte dei Paschi banking foundation - which used to control the bank and now owns just 0.7 percent of it - said on Thursday it would like to wait until after the vote before deciding whether to invest further in Monte dei Paschi.

Morelli, the former head of Bank of America Merrill Lynch in Italy, is aiming to raise the money this year to cover losses from the planned sale of 28 billion euros in gross bad loans.

The CEO told reporters a window existed for the capital increase to start around December 7-8 and to close before the Christmas holidays.

If the plan falls through, Monte dei Paschi would need state support to survive.

Under tougher new European Union rules on bank bailouts, public aid can only come after hitting investors first.

Hundreds of ordinary Italians have already lost their savings in a string of bank crises following a deep recession that saddled lenders with 356 billion euros in soured debts.

Around 150,000 small shareholders hold 55 percent of Monte dei Paschi's capital. Italy's Treasury is the top investor with a 4 percent stake it received as payment for lending the bank money during the financial crisis.

Monte dei Paschi, which has burned through 8 billion euros of capital raised in 2014-2015, worked hard to gather proxy votes and ensure Thursday's meeting reached a necessary 20 percent quorum.

Shareholders representing 22.4 percent of the bank's capital were present at the meeting and the fundraising plan got 96.1 percent of votes.

To cut the size of the new share sale, Monte dei Paschi is offering to convert up to 5.3 billion euros in debt into equity.

Morelli said the swap would be launched on Monday and run for five days if market watchdog Consob approves.

Italian insurer Generali <GASI.MI>, which holds Monte dei Paschi subordinated debt, said on Wednesday it wanted to play a part in finding a solution for the Tuscan lender.

But Morelli said he had not met with the Generali CEO on the matter.

Shares in Monte dei Paschi, which have lost 80 percent of their value this year, closed up 3.3 percent at 0.23 euros.

(Writing by Valentina Za; Editing by Alexander Smith and Elaine Hardcastle)