"The mafia is looking for consensus and is not able to challenge the state today," said Antonio Manganelli, speaking to police trainees in Rome.
''Only when we have found the attacker can we find out what caused him to carry out the attack."
Police are still searching for a middle-aged man captured on security cameras outside the school as he apparently detonated the bomb which exploded at 7.45 am on 19 May as pupils arrived for class.
No group has claimed the blast, which killed 16-year-old Melissa Bassi, critically injured a second female student at the school and wounded several other pupils.
Jailed members of the mafia in the Puglia region where Brindisi is located - the Sacra Colonna Unita - had sent a telegram to Melissa Bassi's family with their commiserations, Manganelli said.
"This was a clear signal that the Sacra Corona Unita was not involved," he stated.
Manganelli also ruled out involvement in the Brindisi blast by an Italian Anarchist group with Greek links that has claimed several attacks in Italy, the Italian Anarchist Federation (FAI).
"I find it hard to imagine that they could have carried out such a cowardly attack," he said, adding that the successors to the Red Brigades, which carried out assassinations in Italy in the 1970s and 1980s were also not suspects in the Brindisi attack.
But Manganelli reiterated earlier warnings concerning the security threat posed by anarchists. "The only structure that carries out terrorist acts is the anarcho-insurrectionist element of the FAI," he said.
Greek anarchist cells were trying create a European network with Italian operatives, he added.
The FAI claimed the kneecapping in May of the head of an Italian nuclear company in the northwestern city of Genoa, and called for "an intensification of the conflict".
FAI claimed responsibility for a package bomb found outside the Greek embassy and defused in December 2010. Nobody was injured in the incident., but two parcel bombs at the Chilean and Swiss embassies in the Italian capital that same month seriously injured two people who opened them.