Police in the Northern Territory should have greater powers to enter homes in child welfare cases, a coroner investigating the murder of two children says.

NT Coroner Greg Cavanagh on Wednesday released his findings into the deaths of Michael Chisholm, Aaliyaha Webb and Julian Chisholm.

Mr Chisholm, 23, smothered to death his eight-year-old stepdaughter Aaliyaha and four-year-old son Julian at his Darwin home in May last year before taking his own life.

"One of the lessons to be learned from this inquest is that additional police powers of investigation for child welfare matters are necessary," Mr Cavanagh said.

A police representative had told the inquest police should be able to enter a premises if they have reasonable grounds to believe they needed to in order to evaluate if a child's welfare was at serious imminent risk.

In his 29-page findings, Mr Cavanagh said mistakes were made by police, who wrongly prioritised a complaint made by the children's mother, Roxanne Lee, on May 21 and did not not send anyone to the premises until the next day.

But Mr Cavanagh did not find police caused the deaths and said it was unknown if the outcome might have been different if police had responded earlier.

The inquest had heard that Ms Lee, who was in a custody dispute with Mr Chisholm, had gone to a police station about 6.30pm on May 21 when she realised the children had not been taken to school and urged officers to check on them.

But the officer on duty ignored his training and Ms Lee was sent away to phone police instead.

Police did not go to the home until the next day, when they found the bodies.

It is thought the children died between 2.30pm on May 21 and the early hours of May 22, and Mr Chisholm then took his own life.

Since the deaths, steps had been taken to improve police processes.

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