Mandela, South Africa's first black president, was admitted to hospital in Pretoria on June 8 for the third time this year, with a recurring lung infection.
"Former President Mandela remains in a critical condition in hospital. The doctors are doing everything possible to ensure his well being and comfort," Zuma said in a televised address to the nation.
Zuma said Mandela's health had deteriorated over the weekend, after he visited the icon's bedside late Sunday.
"Given the hour that we got to the hospital it was late, he was already asleep," Zuma told reporters. "(We) saw him and then we had a bit of discussion with the doctors and his wife Graca Machel."
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Zuma declined to give details about the health of his predecessor even as a jittery nation prayed for its hero, who spent 27 years in jail battling the apartheid regime.
Earlier, Zuma's spokesperson Mac Maharaj had said Mandela's health suddenly deteriorated.
"The condition of former president Nelson Mandela, who is still in hospital in Pretoria, has become critical," said Maharaj.
Zuma, accompanied by African National Congress Deputy President Cyril Ramaphosa, visited Mandela last evening.
"They were briefed by the medical team who informed them that the former President's condition had become critical over the past 24 hours," a statement from the Presidency said.
The statement on his health came amid a mounting public outcry after it was learnt that the ambulance transporting Mandela to the hospital from his home in Johannesburg in the early hours of June 8 broke down and paramedics had to treat him for almost forty minutes before a second one arrived.