Speaking at Mandela's state funeral in Qunu village in the Eastern Cape province, Zuma also thanked the Mandela family for their perseverance over the years when the world icon spent 27 years in jail during the apartheid regime, South Africa's government news agency SA News reported.
"As your journey today, ours must continue. One thing we can assure you today, as you take your final steps, is that South Africa will continue to rise," Zuma said.
Zuma also thanked the Mandela family for their perseverance over the years.
"Your revolutionary spirit will not rest within us. We plan to take your vision forward of better schools, universities, quality housing... decent jobs and as well as an efficient and accountable public service."
In a packed marquee - filled with VVIP dignitaries, including current and former heads of states, royal families and high-profile celebrities - Zuma said Mandela's love for children would be carried forward.
Zuma also thanked Mandela for his sacrifice in the fight against the apartheid government in what led to South Africa giving birth to democracy in 1994.
Describing Mandela as a "fountain of wisdom, pillar of strength and a beacon of hope", Zuma said Mandela taught the country to live together, regardless of race.
Mandela, South Africa's first democratically elected non-white president, died of illness in his Johannesburg home Dec 5 at the age of 95.