The 24-year-old became furious on Sunday when he allegedly punched and kicked the children so hard as to cause the boy’s death, at their house in Cardito, Naples.
Badre reportedly said to police that he was angry that the children had damaged part of a new bed because "we had made sacrifices to buy it".
He also broke a broom in anger, but denied using it against the children.
The girl reported serious but not life-threatening injuries.
The children’s four-year-old sister and mother remained uninjured.
The Naples North Public Prosecutor is investigating further the role of the children's mother, who failed to report the attack to police, possibly out of fear.
She may be denounced for failing to take adequate measures to prevent the violence.
