"About 70% of the agenda of the UN security council is taken up by issues from the African continent," Zuma said.
"The security council has to be expanded in both categories, with at least two seats for Africa in the permanent category and five in the non-permanent category."
The presidency said on Friday that Zuma had returned from New York, where he was attending the 67th session of the UN general assembly.
He was accompanied by International Relations Minister Maite Nkoana-Mashabane, Justice Minister Jeff Radebe and Defence Minister Nosiviwe Mapisa-Nqakula.
Zuma was appointed to serve in UN secretary general Ban Ki-moon's Education First initiative, which was launched on Wednesday.
While in the United States the president also attended meetings on the side-lines on the general assembly.
These included meetings on Somalia and the Sahel region.
Zuma said: "The Somali leadership is expected to play a very critical role in developing a vision that will serve to rally Somali stakeholders and international partners in our efforts at post-transition development."
South Africa was committed to working with Somalia to strengthen relations between the two countries, he said.
Zuma encouraged the international community to assist the people and government in the Sahel region in dealing with the challenges of drug trading, terrorism and the deteriorating humanitarian situation. – Sapa