Zuma said: "If the law is not enough, let us take it to the point. If the constitution is not enough, let us take the constitution to the point."
Zuma, who was buoyed by the warm welcome he received from the young crowd, said he was not done with his fight for liberating poor black South Africans.
He encouraged young people to study and to fight for radical economic transformation.
"I'm very clear that political freedom without economic freedom is not a complete freedom. I think my view is correct."
The strong show of support was in stark contrast to the cold reception he received at a Youth Day celebration in Ventersdorp, in North West, on Friday, where a group of students chanted "Zuma must fall".
In her speech Durban mayor Zandile Gumede tried to woo the youth by turning her attention to issues affecting them.
These included high data costs, student accommodation and joblessness. She said Durban was ready to become a more Wi-Fi- friendly city.