A statement from Mac Maharaj, spokesman for President Jacob Zuma, said the 94-year-old former leader spent a restful night and was "in good hands."
Mandela was admitted to a military hospital in Pretoria on Saturday for tests. The government has offered no details of those tests, but media reports said Mandela was hospitalized after he stopped communicating.
South African Defense Minister Nosiviwe Mapisa-Nqakula, who visited Mandela in the hospital Monday, told journalists that he was "doing very, very well."
"And it is important to keep him in our prayers and also to be as calm as possible and not cause a state of panic because I think that is not what all of us need," she said.
Zuma visited Mandela -- affectionately known in South Africa by his clan name, Madiba -- on Sunday morning and issued a statement that he was comfortable and in good care.
"The Presidency thanks members of the public for the messages of support to Madiba and family. We thank the media and the public for affording him, his family and the medical team the necessary privacy and space," the statement said.
Mandela has had several health scares in recent years, and each time he enters a hospital, South Africans worry. He was hospitalized in February for diagnostic surgery related to an abdominal complaint. In January 2011, he suffered a respiratory infection.
He plays no role in day-to-day politics in South Africa, but is still of enormous emotional importance to South Africans, seen as an iconic liberation hero.
Mandela spent 27 years in prison for his role in fighting the apartheid system. As South Africa's first black president, he symbolizes the optimism that accompanied the African National Congress' election in the nation's first democratic vote in 1994.
Eighteen years later after his election, the ANC is increasingly tainted by corruption and accused by critics of being out of touch with the majority of poor black South Africans.
South Africans have been holding prayer meetings and sending messages to Mandela and his family via Twitter.
However, some South Africans said it was time the country stopped following Mandela's condition so intensively.
"Why won't people just leave Madiba in peace?" tweeted professor Jonathan Jansen, head of the University of the Free State.