The presidency was unable to confirm further details about his condition on Saturday night.
Mandela was admitted to hospital in the early hours of Saturday morning and was treated for a recurring lung infection, the presidency said.
The last update on Mandela's health, released on Saturday morning, said he was "stable" but that his condition was also serious.
The government's choice of words, in particular the use of "serious", was clear cause for concern.
Later, the presidency said Mandela was breathing on his own.
On Saturday afternoon, an ambulance accompanied by a blue light brigade was reportedly seen leaving a Pretoria hospital.
It is not clear whether this was the hospital Mandela was admitted to.
Mandela's wife, Graça Machel, was at his bedside.
"She accompanied him to hospital this morning and she is with him now," said presidency spokesperson Mac Maharaj on Saturday.
Machel had been scheduled to speak at the "Nutrition for Growth: Beating Hunger through Business and Science" summit in London on Saturday.
She cancelled her attendance on Thursday, Maharaj said.
Maharaj did not respond to further questions on Saturday afternoon. In an earlier statement he said the presidency wanted to give doctors the space to treat Mandela without interruptions.
He said doctors were doing everything they could to make Mandela "better and comfortable".
"What I am told by doctors is that he is breathing on his own and I think that is a positive sign," he said. "Madiba is a fighter and at his age, as long as he is fighting he will be fine," Maharaj said.
President Jacob Zuma wished Mandela a speedy recovery.
Regular hospital visits
On April 6, Mandela was discharged from hospital after spending nine days receiving treatment for a recurring lung infection. The Nobel Peace Prize laureate has suffered lung ailments before and has been in and out of hospital.
Early in March, he was admitted to a Pretoria hospital for a scheduled check-up and was discharged the following day.
In December last year, Mandela underwent an operation to remove gallstones and treat the recurring lung infection. He was discharged after an 18-day stay.
In January, the presidency said Mandela had made a full recovery from surgery and continued to improve. In February last year he was admitted to hospital for a stomach ailment.
At the time, the presidency said Mandela underwent a diagnostic procedure to investigate the cause of a long-standing abdominal complaint.
In January 2011, Mandela was taken to Milpark Hospital in Johannesburg for routine tests relating to respiratory problems.
Mandela's last major public appearance was in July 2010 at the final of the World Cup at the Soccer City stadium in Johannesburg.
Since then he had spent his time between Johannesburg and his village of Qunu in the Eastern Cape.
Mandela stepped down as president in 1999 after one term in office and has been removed from politics for a decade.
He appeared in a brief television clip aired by state television in April during a visit to his home by Zuma.
At the time, the ANC assured the public Mandela was "in good shape", although the footage showed a thin and frail old man sitting expressionless in an armchair with his head propped against a pillow. – Sapa, Reuters and Staff reporter