Three-year-old Courtney's body was discovered on May 13 after she went missing nine days earlier.
Mortimer Saunders has been charged with her rape and murder.
On Thursday, Zuma visited the site where Courtney's body was found.
He had earlier visited Courtney's family where he unveiled a plaque.
Addressing media afterwards, Zuma said: “In some cases, by people who are so intimate to us, something has gone wrong. I made a statement this morning and called upon South Africans to unite and fight against this. I think that enough is enough, we cannot allow this to happen.”
Zuma then left the house and drove to nearby Epping where Courtney’s body was discovered on Saturday, nine days after she had gone missing. A memorial site, with a cross and flowers, has been erected at the spot where her body was found. Zuma spent several minutes pensively at the site.
Cape Argus and ANA