The 49-year-old then contacted the local police unit where he worked in a technical role, saying: "Come to my house, I'll leave the door open. I've killed them all," Genova Today reported.
He also told colleagues he was about to kill himself.
Italian media have named the man as 49-year-old Mauro Agrosi, and it is thought that he used his service weapon to carry out the murders, covering the gun with a pillow to act as a silencer.
The triple murder took place shortly before 7am in the coastal Cornigliano district of the Ligurian city where Agrosi lived with his wife and two daughters, aged 14 and ten.
The incident has parallels to a similar crime which took place in the same area in 2003, when a 47-year-old police officer killed his wife and two young children with his service weapon, before killing himself.