Social workers were made aware of nurses' concerns over baby twins Chris and Cru Kahui weeks before the boys died of head injuries.
The 3-month-old boys died in Auckland's Starship Children's Hospital within 13 hours of each other last Sunday, several days after they were taken to Middlemore Hospital by relatives.
Their injuries were multiple and severe and included brain damage and a broken thighbone.
The twins spent six weeks at the KidzFirst neonatal unit at Counties-Manukau hospital after being born prematurely.
The Sunday Star-Times reported today KidzFirst nurses and a social worker had concerns about the boys' parents, Sonny Chris Kahui and Macsyne King, because of the short time they spent with the boys during their time in the hospital.
Nurses raised concerns with hospital social workers but the children were sent home having passed a rigorous monitoring process, the paper said.
A KidzFirst spokeswoman said the fact the parents did not go to the hospital often was not considered abuse, but was "cause for concern".
She said a nurse visited the twins at home the week before they died, when they were judged healthy.
But a hospital social worker was understood to have informally raised concerns with a Child, Youth and Family worker but the alert did not reach the threshold required to constitute a formal notification.
A CYF spokeswoman said the agency was not aware of concerns being raised informally.
Yesterday the boys were buried in a white coffin at Mangare Lawn Cemetery after a tangi at Manurewa Marae.
Police are continuing their appeal to the family -- who are being accused of stonewalling the investigation -- to bring the killers to justice.
For the first time police used the term murder in relation of the babies" deaths.
They were shielding the killer with a pact not to talk to police and help the police investigation, said Detective Senior Sergeant John Tims earlier.
Two or three days before they died, police said the family met in a south Auckland house where the decision was made not to co-operate with police until a family spokesperson or lawyers had given their go-ahead.
That pact meant police could not find out who had inflicted the horrific injuries on the boys or why.
Mr Tims vowed police would not ease up on their double homicide inquiry "until we have found the individuals responsible for the murder of Cru and Chris Kahui".
The father of the dead babies told police he had no idea who inflicted their injuries.
Ms King's lawyer, Marie Dyhrberg, said she was "absolutely committed to doing what she can so that whoever has done this is brought to justice".