In August, Rome signed off on a plan to create a national unified fast broadband network designed in part to head off concern that Telecom Italia (TIM), Italy's biggest phone group, could end up with too much sway over it.
Leaders of the three companies met on Monday with the chief executives of state lender CDP and TIM.
"The three CEOs hope the network plan can be developed in line with its premises, giving rise to a non-vertically integrated operator," they said in a joint statement.
TIM, with a large retail client division, has repeatedly said it wants to control any single grid while European regulations favour the adoption of a non-vertically integrated model outside TIM's control.
Under the government's plan, TIM could have a majority of shares but would not have control of the board, while the grid would have to be open to all operators and acceptable to regulators.
Last week EU antitrust chief Margrethe Vestager declined to comment on the plan to create a single network through the merger of TIM's grid assets and those of smaller wholesale-only rival Open Fiber.
"One can imagine that you have a nationwide wholesaler. That is definitely imaginable ... The question of course is (whether) that is an independent wholesaler or the wholesaler also has ties vertically to retailers," Vestager said.
"That would be a competition assessment and that would be our approach no matter what country it would be concerned with," she said.
(Reporting by Stephen Jewkes and Elvira Pollina; Editing by Dan Grebler)