The ‘End Prostitution Now’ campaign aims to put the focus firmly on those who create the demand by buying sex but who have not been in the spotlight in the past.
Posters highlighting the experience of men who have paid for sex are a feature of the new initiative.
Led by Councillor James Coleman, Depute Leader of Glasgow City Council, the campaign is pushing for amendments to proposed and existing legislation which will create a range of offences designed to target the purchase of sex.
It also aims to raise awareness of the harm caused by prostitution.
West Renfrewshire MSP Trish Godman will be pledging her support to the campaign by proposing legislative amendments in the Scottish Parliament in the coming weeks.
Support has also been building among other MSPs, councillors, unions and faith groups, the city council said.
A dedicated website has also been created so the public can sign up in support of the campaign and call for a change in the law.
Mr Coleman said prostitution was an "appalling form of human exploitation".
He added: "It blights the lives of those involved, their families and the communities where this awful trade takes place.
"Tackling demand is the key to this issue. It is demand which fuels the vicious cycle of sexual exploitation that supplies vulnerable people in to the sex industry."
The campaign is calling for amendments to be made to the Criminal Justice and Licensing (Scotland) Bill, which is currently going through Holyrood.
If included in the legislation, these could allow for premises involved in the 'facilitation of the sale of sexual services' to be closed.
And a new offence of 'facilitation of the sale of sexual services' would be defined using an amendment to the Sexual Offences (Scotland) Act.
Mr Coleman added: "The recent kerb crawling legislation went some way to address demand, but it left significant gaps.
"The amendments we propose will extend the reach of the law so there is no hiding place for the pimps, punters and brothel keepers who prey upon others.
"Treating individuals as commodities to be bought and sold is an attitude which was unacceptable in the 19th century and there is no reason why it should be acceptable now.
"By legislating against demand we will be sending a clear message that people are no longer for sale in this way.
"It is time to assign responsibility where it belongs, with the buyers of sex, and to end prostitution now."
Mrs Godman gave her backing to the campaign and said: "We believe these amendments present a simple but devastatingly effective means of challenging demand for prostitution.
"Introducing these amendments as law would ensure that anyone involved in the purchase, marketing or facilitation of sexual services would be criminalised whether these acts took place on the street or indoors."
She went on: "Every shred of evidence indicates that prostitution is inherently harmful. It is incredible that something which so clearly breaches an individual's right to dignity, equality, respect and physical and mental well-being has gone unhindered for so long.
"We must end prostitution now and these amendments will give us the power to make that happen."
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