Serious criminals may face longer monitoring by the Parole Board after convicted murderer Paul Russell Wilson murdered again last year, eight years after he was released from jail.

Wilson, also known as Paul Tainui, served 16 years in jail after murdering his girlfriend Kimberley Schroder in 1994.

Eight years after he was released in 2010, he murdered 27-year-old Nicole Tuxford in Christchurch last year. In March he was sentenced to life imprisonment for the second murder with a minimum non-parole period of 28 years.

Nicole Tuxford's mother Cherie Gillatt and Kimberley Schroder's modern Nancy Schroder appealed this week to Prime Minister Jacinda Ardern for an independent review of the way official agencies dealt with Wilson since 2010.

"I'm told that the Parole Board commissioned an independent review of their actions," she said.

"While that concluded they took an overall cautious approach to granting parole and proper process was followed, the head of the Parole Board, Sir Ron Young, has since said he disagreed with the report's conclusion that there were no lessons to be learned.

"He has subsequently talked to the justice advisory group about extending the Parole Board's monitoring of serious criminals as a result of this case. I support that sort of thinking."

Wilson continued to be monitored by the Corrections Department under his first life sentence for Kimberly Schroder's murder after the Parole Board's oversight ended in 2011.

Ardern said Corrections had "undertaken an internal investigation and the findings have been shared with Nicole Tuxford's family but have not been made public yet".

"I am also told that the Independent Police Complaints Authority (IPCA) is currently investigating the actions of police," she said.

"I think it's best to allow the IPCA to conclude their investigation and release their findings before any decisions on further action is made."

IPCA manager Dr Warren Young said the authority was investigating a complaint about the actions of police when they stopped Wilson's car at a drink/drive checkpoint the day before he murdered Nicole Tuxford in April last year.

Gillatt and Schroder said police saw that Wilson was carrying two butchers' knives in his car.

"One officer even described a feeling of anxiety and a need to act with caution around Wilson," the mothers said.

"Yet, despite knowing that Wilson had been convicted of a stabbing murder, police took no steps to apprehend Wilson, nor did they even seek advice on what steps they should take."

Ardern acknowledged the two mothers' anguish.

"This is an incredibly tragic case, and I know that everyone involved in it; police, Corrections and the Parole Board have done soul searching as to how Nicole's horrific murder could have been prevented," she said.

"I also want to acknowledge the advocacy of Cherie Gillatt and Nancy Schroder, Nicole Tuxford and Kimberley Schroder's mothers. Both these women have lost so much and understandably continue to question what more could have been done to avoid the senseless murder of their daughters."