The SNP leader admitted the word "national" could be "hugely problematic".
Calls For Domestic Abuse Offence
Creating a specific offence of domestic abuse could help ensure Scotland remains at the forefront of efforts to combat violence against women, one of the country's top prosecutors has said.
Solicitor General Lesley Thomson QC also argued making domestic abuses a specific offence would help victims and could ensure the law "remains fit for purpose''.
She highlighted the need for a more modern approach to tackling the problem as she addressed a special conference organised by the Crown Office and Procurator Fiscal Service (COPFS).
The Crown Office defines domestic abuse as being any form of physical, sexual, mental or emotional abuse that might amount to criminal conduct in a relationship or between former partners.
Police recorded 60,080 incidents of domestic abuse in Scotland in 2012-13, up from 59,847 in the previous year.
Ms Thomson told the domestic abuse conference in Glasgow that Scotland had already "come a long way in dealing openly and honestly with the causes and consequences'' of this type of crime.
She highlighted the introduction of legislation on stalking in 2010 as one example of this, saying it "gave prosecutors a new tool to tackle this harmful behaviour and sent a clear public message that this sort of conduct was not acceptable and would not be tolerated''.
Ms Thomson added: "Domestic abuse is in my view another area in which specialist legislation has a role to play.
"It has the potential to effect further change in societal attitudes, to instil confidence in victims and, of course, to ensure that their abusers are held to account.
"Creating a specific offence of domestic abuse is one way in which we could ensure that our criminal law is and remains fit for purpose.
"It would help victims by acknowledging the true impact and consequences of all types of abusive behaviours, including non violent tactics of control and abuse, and would solidify Scotland's position as a leader in the field of tackling violence against women.''
Justice Secretary Kenny MacAskill said there were already "a range of existing laws that can be used to deal with incidents of domestic abuse such as assault and stalking''.
He stressed tackling abuse was a "key priority'' for the Scottish Government and added work was being done to look at how new laws could help with this.
"It is vital that our police, prosecutors and courts have the powers they need to hold perpetrators of domestic abuse to account,'' Mr MacAskill said.
"The Scottish Government is driving forward work to consider, in liaison with justice agencies and victim support groups, how new laws could help ensure those who commit acts of domestic abuse are dealt with effectively by our justice system.''
Lily Greenan, the manager of Scottish Women's Aid, said while the justice system had improved the way it deals with domestic abuse, there were many cases where it was treated as a "series of minor assaults''.
She added that this approach meant there was only "limited recognition of the enormous impact that years of this kind of abuse has on women and on their children''.
Ms Greenan said: "We believe it is time to address this and look forward to working with COPFS and other partners in the Scottish criminal justice system to continue to improve the response to domestic abuse.
"Acknowledgement of the complexity of domestic abuse within a legal context is a positive move which will benefit women.''
Anne Marie Hicks, the National Procurator Fiscal for domestic abuse, said there had "undoubtedly been a culture change over the years in the way in which domestic abuse is viewed''.
She stated: "I feel proud that by developing our policies and approach to this type of crime so significantly, we have undoubtedly contributed to this cultural and attitudinal shift, and increased public confidence in the criminal justice response.''
Aaron Slater, helpline and support manager for the group Abused Men In Scotland, welcomed the idea that a specific offence of domestic abuse could be created.
He said: "When we are supporting men affected by domestic abuse we talk to them about patterns of behaviour, about control, and about coercion, but this isn't reflected in the criminal law.
"A focus on a single incident lacks context. It does a dis-service to those affected by domestic abuse and their lived experiences.
"We hope that a new approach will help more people have the full extent of their experiences heard and duly acted upon.
"This means that those abusers who are currently slipping through the net will be held accountable for their actions."
A police watchdog probe was launched after the remains of the 52-year-old were found in a house in Dumfries in February last year.
The accident happened at about 7.50pm on Thursday in Moodiesburn, North Lanarkshire.
More than 70 firefighters were needed to bring the blaze under control at Blochairn Fruit Market in the early hours of Thursday.
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