* Elliott steps up campaign to dilute Vivendi influence
* Activist wants changes to board
* Vivendi not convinced plan will create value (Adds analyst, funds, details, sources on CEO, BREAKINGVIEWS link)
MILAN, March 16 (Reuters) - Activist fund Elliott Advisors has written to other Telecom Italia shareholders to call for a "truly independent" board to improve governance, performance and shake up the way Vivendi has run the Italian phone group.
Elliott said "poor stewardship under the Vivendi-controlled board has resulted in deeply troubling corporate governance issues, a valuation discount and strategic failures".
TIM has lost more than a third of its market value since French media group Vivendi first took a stake in mid-2015 and increasingly tightened its grip on Italy's biggest phone group.
Vivendi eventually appointed two-thirds of its board and named its own chief executive as TIM executive chairman, raising concerns among other shareholders and politicians in Rome who consider the company of strategic national importance.
Elliott has already proposed removing some TIM board members nominated by Vivendi, including TIM Chairman and Vivendi CEO Arnaud de Puyfontaine, and replacing them with some well-known figures in Italian business.
Shareholders will vote on the matter on April 24.
To challenge Vivendi's weight, Elliott has been on a charm offensive with some of the biggest institutional investors in Italy and abroad. Yet despite disappointment over Vivendi, fund backing is not a given, two sources close to the matter said.
"We need time to assess Elliott's requests ... the main issue will be that of corporate governance, which is clearly weak," an investor at a major Italian fund said.
The funds are also curious what the new chief executive - a telecoms veteran and dealmaker put forward by Vivendi - will deliver, the sources added.
A Vivendi spokesman said the French group would examine Elliott's comments with an open mind, "while bearing in mind (Elliott is) well known for short-term initiatives."
"We are not sure that their idea of dismantling the company and changing the team will create value," the spokesman said, adding a three-year industrial plan proposed by newly appointed CEO Amos Genish was "solid and very promising".
Elliott, founded by American Paul Singer, said it now holds more than 3 percent of TIM's ordinary shares while, together with financial instruments, its interest exceeds 5 percent.
Elliott said it would urge a new board to convert TIM's saving shares into ordinary ones, a move that would reduce the phone group's debt pile but which Vivendi blocked in late 2015.
A conversion of savers could dilute Vivendi's stake in the former telecoms monopoly to around 17 percent.
Elliott also plans to push for a listing or partial sale of TIM's soon-to-be-created network company (NetCo) and reintroduce dividends which were last paid in 2012. It also proposed the full or partial sale of submarine network unit Sparkle.
TIM approved the move of its network assets into a separate company but said the latter would be fully controlled by TIM.
"We believe widening NetCo's share register would create value for TIM shareholders and might hasten the creation of one single national network," Elliott said.
Any move on NetCo or Sparkle would require state backing given that they are considered of strategic national importance.
That hurdle would be removed if state lender CDP became an investor - an option being considered by Elliott, two sources said.
CDP would automatically become a shareholder if NetCo were to merge with rival Open Fiber, a broadband firm jointly owned by utility Enel and CDP. That idea was favoured by some politicians to avoid duplication and boost investments.
In his presentation last week, Genish did not rule out again proposing the share conversion, paying dividends or selling a stake in NetCo in future, but he stressed any such move would be done at the right time to not compromise TIM's financial health.
Should Elliott push for radical changes immediately, the CEO might find it difficult to remain, one source said.
In the letter, the activist fund criticised Vivendi's track record at TIM, saying the French media group exercised "control without regard for minority shareholders' divergent interests".
This included the plan to create a joint venture between TIM and Vivendi's pay-TV arm Canal+ that is now on hold following objections from some board members, and the alleged conflict of interest among some directors nominated by Vivendi.
Elliott reiterated it does not wish to control TIM, but merely seeks to be a catalyst for change.
TIM shares closed up 0.4 percent, while Vivendi closed down 0.3 percent.
(Additional reporting by Maria Pia Quaglia Editing by Keith Weir and Adrian Croft)