Corrections Minister Anne Tolley is looking at whether high-risk domestic violence offenders can be monitored around the clock.
Under the proposal, she said offenders who repeatedly breach domestic protection orders would be tracked 24 hours a day by a GPS monitoring system which is already used to monitor high-risk sex offenders.
Mrs Tolley told Radio New Zealand's Nine to Noon programme on Thursday she has asked the Department of Corrections to investigate extension of the GPS system as it has been shown to be effective.
The minister said it has been in place for about seven months and monitors about 40 people guilty of sex and violence offences.
Women's Refuge supports the proposal. However, spokesperson Sue Lytollis told Nine to Noon it might not be possible to use the tracking system if the risk to a victim has not been recognised, or charges have not yet been laid.
Ms Lytollis said it can be a challenge to get police, and sometimes the victim, to understand how serious a situation is.
However, the father of a woman murdered by her abusive husband said the monitoring plan would not have saved her.
David White's daughter Helen Meads was shot dead in September 2009.
GPS monitoring would probably be imposed by the courts and parole board following a conviction, but Mr White said his daughter's husband had not faced formal charges until her murder.
Mr White said he would have been able to help his daughter if he had better understood domestic violence and wishes he had called Women's Refuge for advice.
Education for families, victims and police is what will save the lives of women in similar situations, he believed.