By Elvira Pollina and Amy-Jo Crowley

MILAN, Sept 8 (Reuters) - Poste Italiane has raised the cash component of its takeover offer for Telecom Italia (TIM), sweetening terms for shareholders as it seeks to secure control of Italy's former phone monopoly.

Poste, which had previously built a 20% stake in TIM, launched its bid earlier this year as part of a plan to create a national champion in digital infrastructure and services.

But the response from TIM shareholders ahead of Friday's deadline for the bid had been sluggish, with Reuters calculations based on stock exchange data showing Poste had so far secured only an additional 5% of TIM's share capital through the offer.

That prompted state-controlled Poste to increase the cash component of its offer late on Monday by 18% to €1.97 per share, while confirming an exchange ratio of 0.218 newly issued Poste shares for each TIM share tendered.

The revised terms value the offer at €13.15 billion ($15.29 billion) at current market prices, around €550 million more than the previous bid.  

'PRAGMATIC MOVE'

TIM's board of directors unanimously backed the Poste offer in July. 

 However, a portion of TIM's institutional investors, who represent the bulk of the group's shareholder base, viewed the original terms of the offer as unattractive, a source familiar with the matter told Reuters. Poste declined to comment.

 "We think this is a pragmatic move aimed at bringing the TIM deal to a positive conclusion," analysts at broker Intermonte wrote in their daily report, commenting on Poste's revised terms. 

The state-backed conglomerate, which projected annual pre-tax benefits of €700 million from the deal, also waived the 66.67% acceptance threshold it had initially set as a condition for the offer to proceed. It said the offer period would reopen from September 21 to September 25. 

Poste shares were almost flat in morning trade on Tuesday.

TIM shares rose 2.5% to €7.66 by 0830 GMT, with Poste's offer representing a premium of about two euro cents per share.  

At Monday's close, TIM shares were trading at €7.42, implying a premium to the €7.39 value of Poste's initial offer. ($1 = 0.8598 euros)

(Reporting by Elvira Pollina in Milan, Amy-Jo Crowley in London, and Chandni Shah in Bengaluru. Editing by Edmund Klamann, Cynthia Osterman and Keith Weir)

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