Together with F2i, the Milan-based TV group, which already owns 40 percent of EI Towers, has offered 57 euros per share for the rest of the Italian masts group.
The bid represents a premium of 19.2 percent to the weighted average of prices in the six months preceding the announcement, F2i said in a statement.
The group is worth 1.4 billion euros ($1.6 billion) based on Monday's closing price of 49.35 euros a share.
The bid is launched through a special purpose company called 2i Towers, indirectly controlled by F2i.
The sector has been attracting investors looking for infrastructure-based assets that offer steady returns thanks to multi-year hosting contracts.
EI Towers owns and manages the main Italian network for the transmission of the TV signal, a network for the transmission of mobile telephone services and has a fiber optic backbone of over 6,000 km serving its infrastructure.
Under the guidance of a fund, EI Towers could take part in the consolidation underway in the sector.
"EI Towers will acquire the role of independent operator, a status that will make possible to participate more effectively in the process of consolidation in the broadcasting and telephone towers business...," Mediaset said in a statement.
In 2015 EI Towers attempted to take over rival state-owned Rai Way but met resistance from Italy's then centre-left government, which said it wanted to keep a stake of at least 51 percent in the towers unit of national broadcaster Rai.
($1 = 0.8539 euros)
(Additional reporting by Francesca Landini in Milan, Ishita Chigilli Palli in Bengaluru; writing by Francesca Landini; editing by Rosalba O'Brien and Louise Heavens)
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