MILAN, Nov 20 (Reuters) - Telecom Italia (TIM) will hold a second extraordinary board meeting in two weeks on Nov. 26, two sources familiar with the matter said on Saturday, as an internal war over the role of Chief Executive Luigi Gubitosi escalates.

Gubitosi survived a boardroom showdown on Nov. 11 but after two profit warnings this year at Italy's former phone monopoly he remains under fire, having failed to convince top investor Vivendi that he could tackle the company's problems.

The French media giant, which holds a 23.8% stake in TIM, has called into question the role of Gubitosi, pushing to replace him with TIM Brasil head Pietro Labriola, sources have previously said.

Weighed down by an adjusted gross debt of 29 billion euros ($33 billion), TIM is wrestling with fierce price competition on its home turf at a time when it needs to invest heavily to support Italy's drive to improve broadband connectivity.

On Friday, S&P downgraded TIM's long-term rating to BB from BB+ due to the declines in revenue and profit.

The new extraordinary board meeting was called after a letter from a group of five board members close to Vivendi and a separate request from other independent board members, one of the sources said.

Gubitosi had won a second term in March with backing from Vivendi and state lender Cassa Depositi e Prestiti, which owns a 9.8% stake in TIM with the aim to oversee its network assets.

His reappointment was originally part of a broader plan championed by the previous government to merge TIM's access network assets with those of state-backed rival Open Fiber.

However, that plan has stalled with key figures in Prime Minister Mario Draghi's coalition opposing it and question marks hanging over whether it would ever get past regulators in Brussels. ($1 = 0.8859 euros)

(Reporting by Elvira Pollina; Writing by Angelo Amante; Editing by David Clarke and Clelia Oziel)