* Elliott steps up campaign to dilute Vivendi influence
* Activist wants changes to board
* Vivendi not convinced plan will create value (Adds details, quotes, Vivendi comment, shares)
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 top 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 one-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 at a meeting called for April 24.
The activist fund, founded by American Paul Singer, said it now holds more than 3 percent of TIM's ordinary shares while, together with financial instruments, its disclosable interest exceeds 5 percent.
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 added, adding a new three-year industrial plan proposed by CEO Amos Genish was "solid and very promising."
The fund said it would urge a new board to convert TIM's more than 6 billion saving shares into ordinary ones, a move that could help raise cash and 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.
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.
In the letter, the activist fund criticized 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 were up 0.4 percent by 0935 GMT, while Vivendi's shares were down 0.5 percent. (Reporting by Agnieszka Flak Editing by Keith Weir)