John Edwards, who had a history of domestic violence, shot dead 15-year-old Jack and 13-year-old Jennifer at their home on July 5, 2018, before killing himself.

The children's grieving mother Olga Edwards took her own life months later.

NSW State Coroner Teresa O'Sullivan last week found there was a string of critical "errors and omissions" made by police, firearms registry staff and a family court lawyer that led to the deaths.

"The evidence before this court plainly reveals the deaths of Jack and Jennifer were preventable," she said, noting Ms Edwards and the children had disclosed the abuse and violence to multiple agencies.

NSW Police issued a statement on Sunday night after Mr Fuller appeared on Nine's 60 Minutes program.

"The systems, processes and people let Jack, Jennifer and Olga Edwards down, for that I am sorry. We have to take responsibility for their deaths," Mr Fuller said.

"John Edwards should have never got access to firearms. As the NSW Police Commissioner, I need to make sure that can't happen again."

Premier Gladys Berejiklian said on Monday there was always a shared responsibility for such events.

"Nobody wants to see tragedies like that occur and I'm deeply grateful and appreciate the commissioner's comments and I know they were heartfelt," she said.

Around 150,000 people in NSW report family and domestic violence each year, according to police data. Half of all homicides in the state are domestic and family violence-related.

"Whilst we have made significant changes to the systems and processes, 15 recommendations made primarily for the NSW Police Force have been rectified," Mr Fuller said.

The force will review the coroner's findings and consider all recommendations directed to police, including a review of the NSW Firearms Registry.

Since 2018, the registry has undergone an extensive restructure to improve compliance and better identification of breaches of the legislation. More will be done this year.

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Australian Associated Press