Acting operations deputy police commissioner Donald Yamasombi told FM100 News on Saturday afternoon that Tovere died at the Port Moresby General Hospital.
Yamasombie said Tovere was responding to reports of the sale of alcohol at a black market in the settlement when he was attacked.
Yamasombi has appealed to police personnel in Port Moresby to refrain from carrying out any retaliatory acts.
The National newspaper reported that in response to the attack, angry police officers were seen driving in a convoy in Port Moresby yesterday with their sirens blaring. Footage has also emerged of police officers firing gunshots into the air at one location.
Police assistant commissioner Anthony Wagambie told EMTV that some aggrieved officers had engaged in a small confrontation with PNGDF personnel after learning of the death of their colleague.
But he said all officers were ordered back to the Boroko police station where he told them that no one was allowed to enter army barracks.
Wagambie said the PNGDF was working on bringing the perpetrators of the attack to account, and that one suspect had already been identified.
He told media that another officer involved in the attack was on the run, but that the PNGDF "would bring him in".