RAI 1 television quoted prosecutors as saying hooligans, none of whom has yet been identified, chanted slogans with clear extreme-right political connotations.
Another possible charge could be "apology of fascism," a penal crime in Italy which was under the dictatorial regime of Benito Mussolini for two decades in the first half of the 20th century.
Meanwhile ANSA news agency quoted prosecutors in Arezzo as saying they were investigating the police officer on a charge of manslaughter as a result of culpable negligence.
Gabriele Sandri, 26, a Lazio fan heading for a Serie A game in Milan, died at a motorway rest station Sunday morning when the police officer fired warning shots to stop a clash among fans of Lazio and Juventus near the Tuscany town of Arezzo.
The policeman said in a newspaper interview his gun went off as he ran to stop rival supporters fighting.
The unnamed policeman, who has been in the force for 12 years, told the Italian newspaper Corriere della Sera he fired his pistol more than 200 metres away from Gabriele Sandri, who was sitting in a car on his way to see Lazio play Inter Milan.
"I was not aiming anywhere, I was not pointing at anyone," the policeman was quoted by the newspaper as saying.
"The first shot I fired in the air and the second went off as I was running ... Now I have destroyed two families, that of this boy and mine." The fan's death triggered violent clashes around Rome's Stadio Olimpico where the evening game Roma-Cagliari was cancelled due to fear of clashes.
Groups of hooligans, apparently made up of Roma and Lazio fans, clashed with officers Sunday night attacking police offices and the headquarters of the Italian olympic committee (CONI).
CONI reported damage of about 100,000 euros (147,000 dollars) from the raid. Two large glass panes at the entrance and a window were broken and a computer stolen from the building.
Although it appears to be entirely accidental, Sandri's death is considered to be football-related by several commentators.
His killing is the third this year after that of a lower-division team official who was trying to calm down an after-game fight, and the violent death of a policeman in clashes outside the stadium of Catania.