The National Domestic Violence Intervention Agency (NDVIA) said such a move would reflect the seriousness of the problem in Ireland.
The inter-agency body said gardaí responded to around 10,000 calls in relation to domestic violence every year.
NDVIA chairwoman Gráinne Healy called on Garda Commissioner Noel Conroy to “re-prioritise” domestic violence.
“It is now almost 10 years since domestic violence was listed as a priority in the annual policing plan.
“The time in now right to place domestic violence back in the top 10 of priorities for 2006-2007.”
Ms Healy said research conducted in 1999 indicated that one in five women could expect to be subjected to some form of domestic violence in their life.
She said domestic violence was a “form of terrorism” that can include rape.
She said that 108 women had been murdered in Ireland since the start of 1996.
In 65% of cases, the women were killed in their own home. Of the 72 cases resolved, 82% were killed by men they knew with 46% killed by a partner or ex-partner.
NDVIA clinical director Don Hennessy said male offenders groomed their victims before committing any crime.
He said the failure of many women to follow through with complaints was due to the fact that the offender controlled his victim’s response.