MILAN (Reuters) - Activist fund Elliott sought to reassure Telecom Italia chief Amos Genish on Monday that it would work with him to set company strategy, after he said his position would be "untenable" if Elliott succeeded in overhauling the board.

Elliott owns 9 percent of the former state phone monopoly and is calling on other investors to help it wrest control away from French media group Vivendi, which effectively runs Telecom Italia as its top shareholder with a 24 percent stake.

Elliott wants to keep Genish, appointed by Vivendi, but he told Britain's Sunday Telegraph that his position would be untenable if Elliott and its allies secured a majority of board seats at a shareholder vote on Friday.

Genish was quoted as saying that Vivendi's directors were "the only slate to support our long-term industrial plan".

In a statement on Monday, Elliott said its principal aim was to create an independent board and that it only wanted to "enhance" not replace Genish's plan to turn around Telecom Italia (TIM). The stock has lost about a quarter of its market value since Vivendi first took a stake in mid-2015.

"There is no alternative business plan," it said.

"Elliott believes that the management team led by Mr Genish, together with an independent board, should evaluate whether and when to carry out strategic initiatives, in the best interest of value creation for all shareholders," it added.

Elliott and Vivendi have been trading blows for the past eight weeks, with Elliott accusing Vivendi of serving only its own interests and the French media group saying the fund was looking only for short-term financial gains.

Beyond a boardroom shakeup, Elliott has proposed to sell a majority stake in TIM's soon-to-be created network unit, NetCo, and merge it with local rival Open Fiber. It also said TIM's Brazilian unit could be combined with a local peer.

TIM under Genish has said its main objective is to strengthen the firm's finances and operations and reclaim an investment grade credit rating, and that potential asset disposals could help to undermine that goal.

New York-headquartered Elliott Management Corp was founded by U.S. billionaire Paul Singer and manages two funds with combined assets under management of about $35 billion (25.5 billion pounds). Its push for change at Telecom Italia is being spearheaded by London-based affiliate Elliott Advisors (UK).

Elliott has also said it is "deeply troubled" by recent graft allegations involving Vivendi's top investor, French billionaire Vincent Bollore.

Bollore was placed under formal investigations over allegations that his company, Groupe Bollore, undercharged for work on behalf of presidential candidates in two African nations in return for port contracts.

Bollore has denied any wrongdoing.

(Writing by Mark Bendeich)

By Agnieszka Flak