Zuma was due to attend a regional summit in the Mozambican capital Maputo Thursday, but decided to cancel his trip.
President Zuma was briefed by doctors who were doing everything possible to ensure 94-year-old Mandela's well-being, an official statement said.
Earlier this month, Mandela, the country's first black president, was brought to the Medi-Clinic Heart Hospital here for third time this year. He was admitted in a serious condition with a recurrence of long-standing lung problems. He has been in intensive care since.
On Tuesday, a cleric prayed for Mandela's "peaceful end". Also visiting Tuesday was Mandela's daughter Zindzi, who said her father had "opened his eyes and smiled".
The Nobel Prize winner's lifetime of struggle and sacrifice has included a period of 27 years in apartheid jails. His endeavours helped lead to the country's first all race election in 1994, following which he served as country's president between 1994 and 99.
In South Africa's Eastern Cape province, where Mandela grew up, a traditional leader said the time was near for Mandela, who is also known by his clan name, Madiba. "I am of the view that if Madiba is no longer enjoying life, and is on life support systems, and is not appreciating what is happening around him, I think the good Lord should take the decision to put him out of his suffering," said the tribal chief, Phathekile Holomisa.