* FSI agrees first injection of 200 mln euros
* Fibre project open to T.Italia others to join
* Analysts say project could damage T.Italia
MILAN, May 28 (Reuters) - A state-backed Italian fund said on Monday it would invest up to 500 million euros to help fund a project that will bring fibre optic into Italy's main cities, as the country seeks to fill a gap in high-speed internet access.
The 4.5 billion euro project, led by fibre optic company Metroweb and its main investor F2i, is open to other telecom players to join but analysts say it could hit Telecom Italia's monopoly in the country's richest regions.
The Italian Strategic Fund (FSI) said on Monday it had agreed to inject an initial 200 million euros in Reti TLC, the vehicle that controls Metroweb, with an option to pump in a further 300 million euros.
"In this first phase Reti TLC aims to bring fibre to Brescia and Genoa," FSI Chief Executive Maurizio Tamagnini said at a press conference.
Italy lags Europe in terms of broadband penetration with only 49 percent of households connected against a European average of 61 percent, according to Eurostat data cited by Metroweb.
The investment would give FSI, controlled by state financing company Cassa Depositi e Prestiti (CDP), a stake of 46.2 percent in Reti TLC. F2i, the infrastructure fund headed by Vito Gaberale, would retain the majority.
Metroweb covers the Milan metropolitan area with a fibre optic network and its main client is Fastweb, the Italian unit of Swisscom.
In March, Gamberale outlined in parliament the 4.5 billion euro plan, which envisages bringing fibre optic to an additional 10 million people in Italy's 30 most important cities by 2017.
FSI Chairman Giovanni Gorno Tempini said on Monday the development of Reti TLC was intended to be "in synergy with Telecom Italia to create a strategic infrastructure".
Italian newspaper Corriere della Sera said on Saturday that hedge funds were selling shares in Telecom Italia as they expected growing competition from fibre optic group Metroweb.
"A rollout by Metroweb would be damaging to Telecom Italia," analysts at Bernstein said, adding that it would make more sense for Telecom Italia to carve out its infrastructure into a separate company and join Metroweb's efforts.
However, the division of Telecom Italia's debt would make such a move complicated, according to Bernstein.