The Italian Football Federation (FIGC) has suspended next week's Serie B and C matches after the latest fan violence.
Minister Melandri has called for tough action to be taken
On Sunday, games were halted across the country and police attacked after a Lazio fan was shot by a policeman.
Italy's Euro 2008 qualifier away to Scotland on Saturday means there are no top-flight Serie A games next weekend.
But FIGC president Giancarlo Abete has
not ruled out the possibility of the postponements continuing after the
"We don't intend to restart all tournaments from Sunday 25," he said.
"We will have to study, with the Serie A clubs, certain initiatives to be put in place by the 25th - a reflection of the values of football, like a categorical no to any form of violence."
Sports minister Giovanna Melandri had earlier asked for "a strong gesture, in particular suspending the championships for a few weeks".
She added: "Today I think a significant gesture needs to be made to express the condolences from the sporting world and the football world and the shared mourning and at the same time a condemnation without hesitation of violence."
Sunday's incident occurred when Lazio fans travelling to see their team play at Inter Milan encountered Juventus fans at a motorway service station in Tuscany.
Football has a central place in the life of Italy, so whatever problems exist at a social level find their way to the stadium
Uefa spokesman William Gaillard
Lazio's game with Inter and Roma's match with Cagliari were both postponed in the aftermath of the fatal shooting, and Atalanta's game with Milan was abandoned after just seven minutes.
Italy's anti-hooligan body has proposed the banning of large groups of potentially violent away supporters from all grounds.
It has also suggested that away fan attendance should be decided on a game-by-game basis, and wants 'supporter passports' introduced as soon as possible.
Uefa spokesman William Gaillard told BBC Sport that although there was clearly a serious problem, it was unfair to lay the blame entirely at the door of football.
"It reflects social difficulties in Italian cities which have little to do with football, and also the presence of extremists and organised groups do not reflect what the average fan feels about football," he said.
"That bullet could have hit anyone in the parking lot, so it's tragic. Football has a central place in the life of Italy, so whatever problems exist at a social level find their way to the stadium."