On the allegations of racism at the Inter match, Gravina added: "The line must be very tough but here too I invite everyone to make a reflection of respect for the roles.
"We are grateful to the Ministry of the Interior for what they do to ensure the security of the events, as well as to the police bodies that have already arrested three subjects.
"I have to worry about the sport and what emerges negatively is the racist chorus against Koulibaly."
Deputy Italian Prime Minister Matteo Salvini said he will call an emergency meeting in the new year, and wrote on Twitter: "In 2018 you cannot die for a football match.
"At the beginning of the year I will convene the leaders of supporters of Serie A and B clubs... so that the stadiums and the surrounding area will once again become a place of fun and not of violence."
Napoli head coach Carlo Ancelotti wanted the game at Inter suspended because of the abuse Senegal international Koulibaly was allegedly subjected to.
With nine minutes left, Koulibaly was dismissed for sarcastically applauding the referee after a caution, and substitute Lautaro Martinez went on to score a late goal that handed Inter a 1-0 win.
"It's a shame because twice we asked for the match to be suspended for the racist chanting towards Koulibaly," Ancelotti told the club's official website.
"It shook him - he's a good-mannered player and he was bombarded by the stadium. Despite our requests and the chanting, the game wasn't suspended. I think it should have been. Next time we'll stop playing ourselves.
"It was impossible for him to be calm - he cares a lot about the issue of racism and he commits a lot of time to the matter, including in society. What happened is unacceptable - not just for us but for Italian football as a whole."
