"Impose the harshest sentences on such crimes, as part of a concerted campaign to end this scourge in our society," said Zuma in a statement.
Anene Booysen (17) was found by security guards at a construction site in Bredasdorp on the weekend.
She was gang-raped and mutilated, and later died of her injuries in hospital. Reuters reported that she had been cut "from her stomach to her genitals".
Zuma described the crime as shocking, cruel, and inhumane.
"It has no place in our country. We must never allow ourselves to get used to these acts of base criminality to our women and children."
Booysen reportedly identified her attackers before she died at Tygerberg Hospital on Saturday evening.
Doctor describes brutality
Die Burger reported on Thursday on the brutality of her injuries as described by the doctor who treated her. He said that he felt it necessary for the public to know the extent of her attackers' cruelty.
He described in detail how her torso was ripped open, after which one of the attackers stuck his hand in her and ripped out her intestines.
"She lost a large portion of her intestines. That is why she didn't survive," The doctor said.
Another source confirmed the doctor's description. The source said that police who appeared on the scene had to pick up Booysen's intestines which were strewn around her. They were covered in sand.
Arrests
Her 22-year-old ex-boyfriend, Johnathan Davids, was arrested in connection with the crime.
According to a source Boosyen and Davids were childhood friends and visited each other's parents' houses.
Davids appeared in the Bredasdorp Magistrate's Court on Tuesday on charges of rape and murder. He will appear again on February 12.
A second man, aged 21, was arrested in Bredasdorp on Wednesday night.
The Police and Prisons Civil Rights Union (Popcru) said it was satisfied with the progress police had made so far.
"The arrest of two men in connection with this vicious crime should serve as a lesson to rapists and murderers whose aim is to infect our societies with despicable evil," said Popcru spokeswoman Theto Mahlakoana.
The union called on society to stand up against crime and share any information related to the incident with police.
Condemnation
Various other organisations and unions also condemned the crime.
The Congress of the People (Cope) said the brutality of the Booysen attack, allegedly committed by those she knew, was not only shocking but an act of depravity.
"Cope is horrified South Africa has unfortunately and regrettably become the rape capital of the world," said Cope MP Beryl Ferguson.
She said this also proved that the department of women, children and people with disabilities, police, and communities had failed to curb this crime.
"It is also deeply disturbing that neither of the departments seems to have any clue nor even a workable programme to ensure that women in South Africa are protected from rape," she said.
Government expressed shock and outrage at the crime.
"They must face the full wrath of the law… those who molest and abuse children have no place in a democratic South Africa," said Government Communication and Information System acting CEO Phumla Williams. – Sapa