Norfolk Police has said it is "reviewing" its working practices after it emerged that officers failed to respond to a 999 call from a house where four people were later found dead.
It comes after the force previously referred itself to the Independent Office of Police Conduct (IOPC) watchdog following the deaths of Bartlomiej Kuczynski, 45, two young girls believed to be his daughters, and a 36-year-old woman.
Officers discovered their bodies at around 7.15am on Friday after forcing their way into a property in the town of Costessey, near Norwich.
Norfolk Police later revealed a 999 call was made by a man from the house earlier at 6am "to which police resources were not deployed".
In a new statement on Monday evening, the force's chief constable Paul Sanford said he knew "the family and the public will rightly want to know whether there was an ability to prevent this tragedy."
He added: "At this stage, I cannot answer that question. What I can say is that we will be open and honest in the days, weeks, and months ahead, to get the answers to this question."
But Mr Sanford also said that while he wanted to "choose my words carefully," he would "not wait for the outcome of this investigation to review our working practices and that process has started."
He added: "Furthermore, the constabulary is currently undergoing a routine inspection by His Majesty's Inspectorate of Constabulary and Fire and Rescue Services. That inspection includes an assessment of our response to 999 calls.
"Today, I have asked the Inspectorate to consider undertaking a deeper review than the robust inspection already planned, to provide the reassurance that the public and I need in our response to emergency calls."
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Police said on Saturday they were not looking for anybody else in relation to the investigation.
The four who died are all believed to be related to each other.
Post-mortem examinations on the two girls are due to be carried out on Wednesday.