"There is no cause for alarm … he [Mandela] is in the hands of a good medical team," said presidential spokesperson Mac Maharaj on Monday.
An update on Mandela's health would be communicated once his doctors updated the presidency, Maharaj added.
Mandela (94) was admitted to a hospital in Pretoria on Saturday for "medical attention".
At the time Maharaj reiterated that Mandela would "receive medical attention from time to time which is consistent with his age".
Motlanthe cancels visit
On Sunday morning, President Jacob Zuma visited Mandela in hospital and found him "comfortable and in good care", said Maharaj.
He again appealed to the media and to the public to respect the privacy of Mandela and his family. It is believed that he is being treated at One Military hospital.
Deputy President Kgalema Motlanthe reportedly cancelled a planned visit to Mandela at his Qunu home last week, according to weekend reports.
"All I know is that there was a planned visit to Mandela, but the deputy president decided to cancel and attend to state matters," Motlanthe's spokesperson Thabo Masebe told the Sunday Times.
Mandela 'is not well'
A Qunu traditional ruler, Nokwanele Balizulu, told foreign news agency Agence France-Presse she saw Mandela shortly before he was taken to hospital.
"I was called by the Mandela family saying Tata [grandfather] is not well. I rushed there and I saw he is not well," she was quoted as saying.
The Associated Press reported on Sunday that worshippers gathered at the Regina Mundi Catholic church in Soweto to pray for Mandela.
Mandela was admitted to hospital in February this year for a diagnostic procedure, which Lindiwe Sisulu – defence minister at the time – later said was "an investigative laparoscopy".
This hospital visit was marked by much less media speculation than a hospital visit in January 2011, when few updates on his condition were made public – leading to rumours about his condition.
In February the presidency sent regular updates on his condition, but did not say in which hospital he was being treated, probably as a result of a media frenzy outside Milpark Hospital in Johannesburg on the previous occasion.
In 2011, he was in hospital for what the Nelson Mandela Foundation described as "routine checks".
That year Motlanthe eventually broke the silence on Mandela's condition on January 27, when he said Mandela was being discharged to receive home-based care for a respiratory infection.
Another frenzy followed in December 2011 when eNews, in a review of stories of the year, carried file footage of Mandela being taken to hospital in January 2011.
This triggered a flurry of rumours about the former president's health. – Sapa