MILAN, Oct 3 (Reuters) - Italy's Intesa Sanpaolo raised its takeover offer for Monte dei Paschi di Siena (MPS) on Saturday, saying it would pay shareholders a further €800 million ($900 million) in cash if they reject MPS's counter plan.

MPS CEO Luigi Lovaglio is seeking shareholder approval in a vote on October 29 for his strategy opposing the €34 billion share-and-cash offer Intesa announced in June - the biggest transaction so far among a dozen banking deals in Italy over the past two years.

Italian takeover rules require Lovaglio to secure shareholder backing before advancing the counter plan he unveiled in August.

Lovaglio's strategy envisages MPS making two separate all-share takeover bids for wealth manager Banca Generali and rival lender Banco BPM.

If MPS shareholders approve either of MPS' two takeover offers on October 29, that would give Intesa the right to drop its own bid based on the conditions to which the bid is subject, Intesa said.

"Intesa Sanpaolo does not intend to exercise the right to waive the conditions ... and will claim for their non-fulfilment," it said.

Meanwhile, Intesa said it would pay MPS shareholders €1.25 per share, increasing an earlier €1 euro cash component it is offering for each MPS share tendered - on top of the 1.6 newly issued Intesa shares offered for each MPS share they hold.

($1 = 0.8887 euros)

(Reporting by Valentina Za; Editing by Alex Richardson and Susan Fenton)

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