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Speaking on BBC Radio Scotland on Sunday, Mr Brown said the introduction of a stand-alone offence in Scotland would send an “important message” that sexual harassment and violence against women was unacceptable.
He confirmed talks continued between the Scottish Government and Baroness Helena Kennedy QC, who is heading up a working group considering the introduction of a stand-alone offence.
The offence would criminalise serious misogynistic harassment as part of wider proposals under the controversial Hate Crime Bill.
Mr Brown also called on men to challenge "low level” misogyny in workplaces, amid mounting concerns over sexism and misogyny in the police.
His comments follow national outrage sparked by the sentencing of Met Police officer Wayne Couzens, who will serve a whole life order for the kidnap, rape and murder of Sarah Everard.
The tragedy prompted widespread anger and calls from campaigners for to tackle sexual violence and harassment, which is hugely under-reported in Scotland.
Couzens, reportedly known among colleagues as ‘The Rapist’ was linked to a flashing incident in 2015 and two more just days before he killed Ms Everard, according to the police watchdog.
Police Scotland has responded to safety concerns by introducing additional vetting for officers and a new protocol that will see any lone officers approaching women using their radios to dial through to the control room to verify their identity.
But Baroness Kennedy, chair of the Working Group on Misogyny and Criminal Justice in Scotland, said she was tired of hearing police forces say they will “learn lessons” in the wake of the tragedy, claiming institutions often put their own reputations first.
The Labour peer warned that abuse often starts with incidents such as flashing and harassment in public spaces, pointing out that Couzens had already given out “alarm signals” to colleagues.
Baroness Kennedy, who will report on findings into a misogyny offence in February, demanded that police needed to take all women's complaints more seriously as she issued a call for more more officers, increased investment and better training of police and those in the justice system.
Speaking on the Sunday politics show, Sandy Brindley of Rape Crisis Scotland said: "As more details emerge of the Sarah Everard case, the more disturbing it is. Her murder was such an abuse of power by a police officer.
"It is chilling that he was known as 'The Rapist' yet nobody held him accountable.
"Institutional misogyny and sexism is an issue in Police Scotland and was revealed in a survey in the last year. What we need is a zero-tolerance approach and a clear commitment from the police to address these issues.
"We need a complete culture change, where sexist attitudes and behaviour towards women is challenged, in all forms. Time and again, we see convictions of men where his employer or colleagues were aware of his behaviour.
"The criminal justice system is also failing to protect women and deter men. We need a system that doesn't let men guilty of rape walk free.
"If the Scottish Government is serious about improving women's safety, we need to see their response to the Lady Dorrian review."
The cross-justice review group, chaired by Scotland’s second most senior judge, Lady Dorrian, recommended earlier this year the country should have a national specialist court to deal with rape cases.
Opposition parties have also voiced fears over police culture, claiming the force north of the Border has as significant a problem as the Met when it comes to misogynistic bullying, discrimination and sexual predators.
Scottish Tory shadow community safety minister Russell Findlay highlighted a spate of cases involving police violence against women.
They include officers who committed a series of sex attacks and female officers being intimidated after making complaints of sexism or sexual violence against male colleagues.
Mr Findlay said: “If Police Scotland want to maintain trust, they have work to do.
"The first step is to ditch the comfort blanket of secrecy in exchange for a new ethos of transparency in which allegations against officers are investigated timeously and without fear or favour.”
Deputy chief constable Fiona Taylor said: “Police Scotland demands the highest levels of integrity from our officers and staff and when someone fails to meet this standard, we take the appropriate action.
"Progress has been made over a period of years, but there remains much work to do and everyone in policing has a responsibility to lead change.”