Mtshali appeared briefly in the Johannesburg Regional Court on Friday, where his case was postponed to December 10.
The ANC Women's League in Gauteng called for him to receive a maximum sentence.
"He should rot or die in jail," said Bontle Setshogoe the league's greater Johannesburg regional organiser.
"He has right to legal representation, but what about the rights of the victims? We are so angry, the boy does not show remorse."
In a letter addressed to the chief magistrate, the league appealed to the court not to grant him bail.
'Set an example'
"We wish the magistrate to set an example to even those who anticipate doing that, especially during the period of 16 days of activism against women and child abuse," the letter read.
She said the league would attend all Mtshali's court appearances to support victims and speak for defenceless women.
The postponement would allow the police to secure a place for him at Johannesburg Central Prison's high security facility.
Prosecutor Carina Coetzee told the court the facility could only keep Mtshali, 28, for seven days, unless there was a court order prolonging his stay there.
The investigating officer wanted to keep the accused at the facility until an identity parade had been done and DNA samples taken for analysis.
Coetzee further told the court four women had come forward after seeing Mtshali's photograph on television.
Avoided eye contact
During his appearance, a shackled Mtshali avoided eye contact with people in the public gallery. He wore a black T-shirt and had a brown towel draped over his shoulders.
He allegedly targeted young black women aged between 19 and 21 in and around Johannesburg and Pretoria. He would allegedly approach a group of women and invite them to celebrate his birthday with him at a nearby restaurant or bar. He would later ask one of them to accompany him to fetch his sister or a friend, taking a metered-taxi into Hillbrow or central Johannesburg.
He then allegedly lured his victim into a hotel room under the pretext of fetching his sister, the friend, or his luggage, and allegedly rape her.
He was arrested on November 12 in KwaMashu, outside Durban in KwaZulu-Natal.