The broker also cut its target price on TIM by 7 percent to 0.66 euros. The shares traded at 0.75 euros at 0810 GMT, down 1.4 percent after earlier slipping by more than 2 percent.
Activist fund Elliott wrested board control from top shareholder Vivendi earlier in May after a two-month campaign but the outlook remains challenging for the former state phone monopoly.
"Mix a looming price war, political interferences, governance conflicts, forex headwinds and you will end up with a toxic cocktail. This is what is on the menu for Telecom Italia ," Berenberg said in a note.
The May 4 shareholder vote, through which Elliott secured 10 or two-thirds of available board seats, was supposed to give TIM a more independent board and loosen the grip media group Vivendi has had over the company.
But the French investor, which owns 24 percent, on Thursday said a "risk of a dismantling" of TIM could prompt the company to call another shareholder meeting to change the Italian phone group's board.
Beyond a governance overhaul, Elliott has proposed a spin-off and partial sale of the soon-to-be-created network company, a conversion of savings shares, a return to dividends and asset sales. But it recently added it would be up to the new board and management to decide whether and when to consider such actions.
"Investors should take (Vivendi's) threat seriously and factor in that it indicates the likely reluctance of Vivendi to accept the long-awaited conversion of the saving shares and it could trigger management instability at TIM," Berenberg added.
Vivendi's threat offered a striking contrast with comments made earlier on Thursday by TIM's boss Amos Genish, who said he had the full confidence of the board to push through with an ambitious three-year business plan unveiled in March.
Genish said none of the proposals made by Elliott were being discussed, stressing that towers unit INWIT and TIM's Brazilian unit were strategic and not for sale.
The Israel-born executive has made staying on as CEO conditional on being able to execute the new strategy focusing on a digital transformation of TIM, fixing its finances and getting back investment grade credit rating.
Following Elliott's proxy fight, investors are again focusing on TIM's operational challenges, including its 25.5 billion euros ($30 billion) of net debt and new rivals appearing in broadband and mobile.
A headache is the pending arrival in Italy next month of French rival Iliad, which is likely to pressure margins.
(Reporting by Agnieszka Flak; Editing by Keith Weir)