The Italian newspaper La Repubblica has compared the scenes to "urban warfare". The violence is believed to have taken place at the Drunken Ship pub - images on La Repubblica's website appear to reveal the damage.
The Lazio fans were reportedly armed with knives, baseball bats, belts and knuckle dusters and they went on to "destroy" the venue. One witness told the paper: "We feared the worst."
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The eight-month-old female pup, which was severely underweight and dehydrated, was asleep in a dining booth.