Scots Conservative leader Ruth Davidson yesterday urged First Minister Alex Salmond to extend "Clare's Law" to Scotland.
The legislation is about to be rolled out across England and Wales after a series of pilot schemes.
Speaking during First Minister's Questions yesterday, Ms Davidson told MSPs: "It is clear from the results that the four pilots were a success. In fact, a third of applications saw relevant information being disclosed."
She said the law would give people in England and Wales the right to information "which could save them from abuse".
"That same right would be of benefit to Scotland," she added.
Mr Salmond - who has promised to consider the impact of the law - said: "The matter is indeed under assessment. We are considering whether this can be extended to Scotland and we will do what we can to ensure that people in Scotland, women in Scotland, are as safe as they possibly can be in the home environment and outside the home environment."
Clare's Law is named after Clare Wood, 36, who was strangled and set on fire by her ex-boyfriend George Appleton at her home in Salford, Greater Manchester, in 2009.
Miss Wood, a mother-of-one, had met Appleton on Facebook, unaware of his horrific history of violence against women, including repeated harassment, threats and the kidnapping at knifepoint of one of his ex-girlfriends.
The victim's father, Michael, originally from Aberdeen, said he was delighted when Home Secretary Theresa May announced the law will be rolled out earlier this month.
There are 60,000 cases of domestic abuse recorded in Scotland each year, Ms Davidson told MSPs, and one in five women will be a victim during their lives.
The First Minister's spokesman said later that separate pilot schemes may be required in Scotland before legislation could be rolled out across the country, potentially delaying the measure further.
But Ms Davidson called for a Clare's Law to be included in the Criminal Justice Bill currently going through Holyrood.
She added: "Alex Salmond has to act now to give people in Scotland the rights and protection they deserve to prevent them becoming victims of domestic abuse."