* TIM proposes to put network into separate, fully-controlled firm
* Italy govt calls project "momentous turning point"
* Shares rise 6 pct on valuation hopes (Recasts, adds details throughout, analyst, updates shares)
ROME/MILAN, Feb 7 (Reuters) - Telecom Italia (TIM) moved closer to splitting off its network business on Wednesday with the presentation of a plan to the government that could mark a turning point in strained relations between Italy's largest phone group and Rome.
The company's shares rose 6 percent, putting them on course for their biggest one-day gain since July 2016, with analysts citing expectations of better TIM-government relations and a chance to unlock value at the telecom company.
Bernstein analysts wrote in a note that the move "would force investors to confront the substantial valuation discount currently being applied to Telecom Italia."
TIM has been under pressure for years from Italian politicians, regulators and rivals to separate and upgrade its network, its most prized asset which analysts have valued at up to 15 billion euros ($18.53 billion).
Pressure on TIM to act intensified after French media group Vivendi, the Italian phone group's biggest shareholder with a 24 percent stake, began to exert greater influence, which upset the Italian government.
TIM Chief Executive Amos Genish held talks with Industry Minister Carlo Calenda on the idea of voluntarily putting the network into a legally separate company fully controlled by TIM.
"This is a momentous turning point after talking for 20 years of the need to separate the network assets and to grant equal access to all operators," said Calenda, who has repeatedly said TIM should unbundle its network and services operations.
Italy said last year it wanted a say in TIM's strategic decisions such as mergers or selling assets it deemed to be of strategic importance, under a so-called "golden power" decree, seen as a move to rein in Vivendi's influence.
Genish said the meeting with Calenda had been "very positive", but also said the plan - aimed at guaranteeing quality of the network, equal access to all and future investments in ultrafast broadband rollout - was at an early stage and needed to be examined by the company's board.
Calenda said Rome would evaluate details of the "complex" operation with Italy's communications regulator AGCOM, which already discussed the matter with Genish last week.
Calenda said it was too early to speculate on the idea of the network company being potentially listed on the stock market further down the road and opened up to new investors.
Italy's biggest phone group is vertically integrated, meaning it gives rivals access to its infrastructure, but also competes with them.
There have been calls from various political circles to merge TIM's network assets with others, especially the fiber optic cable being rolled out by Open Fiber, to avoid unnecessary duplication and save costs.
Genish said that "at this stage" the network company would be fully controlled by TIM. In November, he said TIM wanted to keep control of the network, but did not need to own it in full, adding the company would make a decision "on our terms when we really believe it's needed".
TIM has been discussing a possible separation of its network for years, but the project never took off due to disagreements over its valuation and governance issues.
If the plan goes ahead, it could prove a positive step for a company already battling with huge debts, new competitors in both broadband and mobile and a business in Brazil that is still recovering from economic ills.
"Is management trying to force a debate around valuation? Maybe. If true, well-executed and done at a sensible value, this may represent a long-awaited re-rating catalyst for long-suffering shareholders," Bernstein said.
TIM is due to present a new business plan on March 6.
($1 = 0.8097 euros)
(Additional reporting by Giulia Segreti. Editing by Louise Heavens and Jane Merriman)