Mr Zuma said doctors were doing everything possible to help the former president feel comfortable on his 17th day in a Pretoria hospital, but refused to give details of Mr Mandela's condition, saying: "I'm not a doctor."
Mr Zuma, who previously gave an overly sunny view of Mr Mandela's health, briefly spoke of his visit on Sunday night to the hospital in the Johannesburg. hours.
"It was late, he was already asleep," Zuma said. "And we then had a bit of a discussion with the doctors as well as his wife, Graca Machel, and we left."
The president said South Africans should accept that Mr Mandela is old, and he urged people to pray for their former leader.
"Madiba is critical in the hospital, and this is the father of democracy. This is the man who fought and sacrificed his life to stay in prison, the longest-serving prisoner in South Africa," Mr Zuma said, using Mr Mandela's clan name.
Family members continued with visits to Mr Mandela. They included his former wife, Winnie Madikizela-Mandela.
Monday also marked the 18th anniversary of Mr Mandela's appearance at the 1995 Rugby World Cup final in Johannesburg, a day still enshrined as a hugely significant moment for South Africa.
In a move crucial in unifying sections of a previously fractured society, Mr Mandela wore a green and gold Springboks rugby jersey at the June 24 final in Johannesburg and brought all South Africans together in support of their national team - once an all-white bastion of the apartheid regime and hated by blacks.
He shook hands with and patted the shoulder of the Springboks' captain, Francois Pienaar, after South Africa won a tense final against New Zealand, underlining the new president's dedication to reconciliation.
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