MILAN, Nov 29 (Reuters) - Italy"s Democratic Party (PD) has pledged to actively involve the coalition government in deciding the future of Telecom Italia (TIM) after the country"s biggest phone company lost its fourth chief executive in six years, unions said on Monday. Luigi Gubitosi stepped down as CEO of the former state monopoly on Friday following a clash with its biggest investor, Vivendi (VIV.PA), a week after U.S. fund KKR (KKR.N) submitted a $12 billion proposal to take TIM (TLIT.MI) private. PD leader Enrico Letta said at the weekend that a foreign presence in a strategic asset such as TIM raised concerns. He pointed to what he said were close ties between Vivendi, which is controlled by French billionaire Vincent Bollore, and far-right commentator Eric Zemmour, who is a potential candidate in France"s presidential election next year. Vivendi declined to comment. PD sources said the party, which is a key member of Italy"s broad ruling coalition, would push for the government to take a stand on TIM"s network, the country"s main telecoms infrastructure. During his three-year tenure, Gubitosi secured union backing for a plan to create a single, ultra-fast broadband network in Italy as the best way to protect 42,500 domestic jobs. But the project has run aground under Prime Minister Mario Draghi, with Innovation Minister Vittorio Colao, a former Vodafone executive, favouring a competitive approach. "Despite it being considered strategic infrastructure ... no government has ever taken a brave and clear position on the network," the UILCOM union said in a statement following a meeting between union representatives and PD leaders. "We need politics to step in and place the network under state control ... we"re glad PD leader Enrico Letta told us the government cannot be a spectator this time round, but a leading actor," it said. Crippled by a mountain of debt that successive post-privatisation takeovers have lifted to four times its core profit, TIM cannot shoulder the investments needed to upgrade its network and meet surging demand for connections. KKR, which has a stake in TIM"s last-mile network, plans to carve out TIM"s grid if its bid is successful, sources have said, giving state investor CDP a key role in overseeing it. The government has welcomed the U.S. fund"s interest, saying its stance hinged on plans to secure the investment needed in TIM"s grid and to protect employment. Shares in TIM closed down 2%, bucking Milan"s 0.3% rise (.FTITLMS). TIM has appointed head of TIM Brasil (TIMS3.SA), Pietro Labriola, as general manager, placing oversight of the group"s strategic assets in the hands of Chairman Salvatore Rossi and setting up a special committee to study the KKR bid. The committee could meet on Friday when a board meeting could also take place, a person familiar with the matter said. Gubitosi remains a board member, and two sources close to the matter said the new leadership arrangement was precarious, adding that Labriola"s mandate only ran until July. ($1 = 0.8861 euros)