Police acknowledged that they had spoken to several other family members who had been working well with officers.
But Tiernan said it was disappointing others within the family were not.
Oranga Tamariki received anonymous report of concern before death
"This is disappointing for police and I urge anyone who is approached in this investigation to consider speaking with us so we can establish what exactly happened."
It has also been revealed that Oranga Tamariki received an anonymous report of concern in relation to the baby boy.
Deputy chief executive for Oranga Tamariki, Glynis Sandland, said they became involved shortly before the boy died.
"We were looking into these concerns and working with the family to gather further information," she said.
A number of other children who live at the property where the boy was fatally injured have also been removed.
"I can confirm the other children in the home are with wider family members and there are supports in place to keep them safe," Sandland said.
Tiernan said they were committed to holding whoever was responsible for the baby boy's death to account.
Anyone with information is asked to call the investigation team on (09) 261 1321, Police on 105 or CrimeStoppers anonymous on 0800 555 111.