Labour's claim that police were given orders to pick and choose the cases they pursue is "gutter politics" designed to score points from the recent shooting of two children, Police Minister Anne Tolley says.
Dunedin man Edward Livingstone, 51, shot and killed his children after turning up at their mother Katharine Webb's house in the harbourside suburb of St Leonards with a can of petrol and a shotgun last Wednesday.
He used a secret key to get inside, where he killed Bradley, 9, and Ellen, 6 as they lay in their beds. Livingstone's body was found in the house.
Webb had a protection order against Livingstone but the former Corrections worker breached it twice and was known to police.
Labour party police spokeswoman Jacinda Ardern said claims Government cuts had put pressure on police to not pursue certain cases required a response from the minister.
Ardern went on to say that although there was no evidence that had actually happened, it was "disturbing" to hear anecdotal stories.
"While I have heard similar stories, finding evidence of what are allegedly verbal instructions is difficult," she said.
"In real terms, the police budget has been reduced. It would be disturbing if that has resulted in management telling officers not to pursue cases."
Tolley said she was appalled at the claims.
"Labour has made wholly inaccurate and false claims around the pursuit and prosecution of cases," Tolley said.
"I am disgusted that they would stoop so low, and try to use this terrible tragedy for political ends," she said.
"Police twice arrested the offender responsible for this shocking crime.
"The full facts are still to emerge, and a police investigation is continuing."