It follows the conviction of Iain Packer who was jailed for life with a minimum term of 36 years on Wednesday after being found guilty of murdering the 27-year-old in 2005.
He was also convicted of 11 rapes and 21 further charges including sexual assaults and abduction involving multiple women over 26 years.
Scotland’s Justice Secretary Angela Constance said: “Our thoughts are with Margaret Caldwell and Emma’s friends for their tragic loss, and to the many victims in this horrendous case.
“For Margaret Caldwell and the other victims in this case, justice has taken far too long.
“The only way we can fully protect women and girls and end violence is through fundamental societal change – a change in the actions and behaviour of those who perpetrate violence and abuse and to address and root out the causes of that violence, including toxic masculinity and gender inequality, that leads to violence, harassment, misogyny and abuse against women.”
She added: “As the First Minister has very clearly stated, we are giving serious consideration and are open to a judge-led public inquiry.
“He was also clear that he wants to hear directly from Margaret Caldwell before we take any decision and the First Minister and I will meet with her next week.”
Police Scotland has apologised to the family of Miss Caldwell and Iain Packer’s other victims, admitting they were “let down” by policing.
Solicitor Aamer Anwar, who has represented Emma Caldwell’s mother Margaret Caldwell since 2016 – said his client is looking forward to meeting with the First Minister next week.
Mr Anwar said he will meet with Humza Yousaf and Justice Secretary Angela Constance next week to reiterate calls for a judge-led public inquiry.
The solicitor said the failures to investigate Miss Caldwell’s murder was “the worst scandal to ever hit our justice system”.
He told the PA news agency: “We welcome the First Minister agreeing to meet with Emma’s mother Margaret, Emma’s brother Jamie and myself next week.
“As Margaret said after the verdict, the police have apologised after nearly 19 years, but that is not good enough. In that time six of the 25 victims died never to see justice. How many more do we not know of?
“For Emma’s family, nothing less than a fully independent public inquiry will suffice – this is the worst scandal to ever hit our justice system and the police or Crown Office cannot be allowed to investigate itself, escape scrutiny or accountability.
“Mrs Caldwell looks forward to meeting with Mr Yousaf and says that if he genuinely cares about the victims then he has no other option but to organise a judge-led public inquiry that acts without fear or favour – that is the very least her Emma and the many women who spoke up deserve, for far too long those in the police or Crown who failed them remained in the shadows.
“For Margaret only a public inquiry can reveal the corruption, the criminality and the motivation. Accountability, that is what the police and the Crown always fear, and they cannot be allowed to dictate the terms as they have done for over 18 years.”
