The SNP leader admitted the word "national" could be "hugely problematic".
Claire's Law Allows Abusive Pasts To Be Disclosed
People will be able to find out if their partner has a history of domestic abuse under a police scheme to cut offending.
It comes after a successful trial of the scheme, known as Clare's Law, in Ayrshire and Aberdeen since November last year.
It is named after Clare Wood, who was murdered by her ex-boyfriend in Salford, Greater Manchester, in 2009. A similar scheme was rolled out in England and Wales earlier this year.
The aim is to provide a formal route for people to find out if their partners have a history of domestic abuse.
During the Scottish trial 86 requests were made to police with 35 disclosures made.
Deputy Chief Constable Rose Fitzpatrick said: ``Domestic abuse affects all our communities. Our role is bringing offenders to justice and working with partners to ensure that victims are protected and receive the right support.
''Up to 25% of police time is spent responding to domestic incidents with nearly 60,000 incidents recorded by Police Scotland officers last year.
''When people form new relationships, there can be concerns that the new partner may have an abusive past. This scheme gives people the opportunity to ask that question.
''We want to stop domestic abuse in all its forms and this scheme takes us closer to that aim. Help is also available for the abuser. They have the opportunity to take responsibility for their actions. If they don't, we will.
''We will investigate all reports of domestic abuse and those responsible will face the consequences of their actions.''
Justice Secretary Michael Matheson said: ''Domestic abuse is an appalling crime and I am delighted that, as a result of the national roll out of the scheme, people across Scotland who suspect their partner may have a violent past will have the right to ask for information.
''The results of the pilot clearly show that the scheme works well and is a good fit for Scotland's unique justice system.
''Put simply - it can save lives and sends a clear message that abusers can no longer hide.''
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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