Senior gardaí said they are keeping an open mind. An incident room has been set up as part of the investigation and forensic examinations were under way at the scene.
The man’s partner Kelly O’Brien, 28, escaped through an upstairs back window but suffered injuries including a broken leg and is being treated at Kerry General Hospital.
It is believed Mr O’Brien helped his partner out through the window and returned to save their daughter.
Firefighters who entered the burning house found both of them together, deeply unconscious. Attempts to resuscitate them failed.
The family had moved into the semi-detached two-storey house in the private Killeen Heights estate over a year ago, while awaiting the completion of a regeneration project in the town centre by Tralee Town Council. Mr O’Brien was known to gardaí.
Neighbours spoke of seeing Nadine, who attended Gaelscoil Mhic Easmainn in Tralee, learning to cycle on her pink bicycle.
Mayor of Tralee Grace O’Donnell said the community was deeply sorry at the deaths and would rally around the extended family.
“The people of Tralee will be there to help in whatever way we can.”