President Jacob Zuma issued a statement responding to what he said were inaccurate media reports Mandela had been discharged.
"Madiba is still in hospital in Pretoria, and remains in a critical but stable condition. At times his condition becomes unstable, but he responds to medical interventions," Zuma said, using Mandela's clan name.
Mandela, 95, was hospitalized in early June because of lung problems.
He was 75 when he became South Africa's first black president in 1994, after having spent 27 years in prison, mostly on Robben Island.
He has rarely appeared in public in recent years.