After a board meeting, TIM said it would seek a new round of proposals from CDP and Macquarie, as well as from rival suitor KKR by April 18.

CDP, which owns a 10% stake in TIM, submitted a non-binding bid earlier in March together with partner Macquarie as part of a plan to combine the network assets with those of TIM's smaller rival Open Fiber.

CDP and Macquarie are both investors in Open Fiber. The joint offer values TIM's grid at some 18 billion euros ($19.3 billion), including debt, sources have said.

KKR, which already owns a minority stake in TIM's grid, offered up to 20 billion euros, including a 2 billion euros earnout mechanism - a valuation which was also billed as too low by TIM last month.

The sale of the grid is a key plank of TIM CEO Pietro Labriola's plan to revamp the former national phone monopoly and cut its 25 billion euros debt pile.

(Reporting by Elvira Pollina; Editing by Keith Weir)