The Monte dei Paschi bank headquarters is pictured in Siena August 16, 2013. REUTERS/Stefano Rellandini MILAN (Reuters) - A delay to vital fundraising at Banca Monte dei Paschi di Siena has increased the risk that Italy's third-biggest bank has to be nationalized, a move the government would like to avoid.

Shareholders led by the biggest investor in the bailed-out bank rejected plans for a 3 billion euro ($4 billion) share sale in January and postponed the capital raising until after May 12.

The bank's chairman and its chief executive may resign following the unprecedented clash with the main shareholder in the Siena-based lender, a charitable banking foundation with close ties to local politicians.

The focus of attention now turns to Rome where both the economy ministry, which has oversight of banking foundations, and the Bank of Italy are closely following events.

The world's oldest bank needs to tap investors for cash to pay back 4.1 billion euros in state aid it received earlier this year and avert nationalization after being hammered by the euro zone debt crisis and loss-making derivatives trades.

The capital increase is part of a tough restructuring plan agreed with the European Commission in order to receive clearance for the state bailout.

A Treasury spokesman said the government's priority was to give the bailout money back to taxpayers and it had no interest in nationalizing Monte Paschi, ANSA news agency reported on Sunday evening. Sources said the Treasury will continue to encourage all parties involved to find a solution, ANSA reported.

Monte Paschi Chairman Alessandro Profumo, an internationally respected banker who was formerly the chief of UniCredit , said on Saturday he and chief executive Fabrizio Viola would decide whether to step down next month. A board meeting is expected around mid-January.

Profumo and Viola had already secured a pool of banks to guarantee the rights issue, but only if it was carried out by the end of January.

They said the delay makes fundraising harder because of likely competition from other Italian and European lenders prompted to seek new capital by an upcoming sector health check, and could precipitate the Tuscan bank's nationalization.

By forcing a postponement of the rights issue, the cash-strapped Monte dei Paschi foundation - whose stake in the bank is big enough to veto any unwanted decision - is hoping to win more time to sell down its 33.5 percent holding and repay its own debts.

The foundation head Antonella Mansi said that carrying out the capital increase in January would massively dilute the foundation's holding, leaving it with virtually nothing to sell to reimburse debts of 340 million euros.

($1 = 0.7258 euros)

(Reporting by Valentina Za; Editing by Erica Billingham)