President Jacob Zuma visited Mr Mandela in hospital and said he "looks well".
Mr Zuma said he had been reassured that Mr Mandela was in the hands of a competent medical team at the hospital in Pretoria.
The 94-year-old was admitted to hospital on Saturday to undergo tests.
The continued uncertainty about Mr Mandela's health prompted worshippers to gather yesterday morning at the Regina Mundi Catholic church in the Soweto area of Johannesburg.
The church was a centre of anti-apartheid protests and funerals.
"Yes, it really worries us because he is a great person," said churchgoer Shainet Mnkomo as she left an early-morning service. "He did so many things to the country, he's one of those persons who we remember most."
The Congress of South African Trade Unions said it hoped the government's statement about his condition was true, and urged Mr Mandela to "Get well and continue to inspire us".
Mr Mandela was taken from his home in the rural village of Qunu, in Eastern Cape province, to hospital in the capital on Saturday.
The decision to move him was taken so quickly that some family members and his own foundation were initially unaware it had happened.
Mr Zuma's office said Mr Mandela was doing well and there was "no cause for alarm", but did not give details about the reasons for his admission.
Mr Mandela needs medical attention "from time to time which is consistent with his age", the statement added.
Mr Mandela, who spent 27 years in prison for fighting racist white rule, became South Africa's first black president in 1994 and served one five-year term.
He later retired from public life to live in his remote village of Qunu, in the Eastern Cape area, and last made a public appearance when his country hosted the 2010 World Cup.