The 94-year-old had been admitted to hospital on Saturday to undergo tests.
A spokesman for President Jacob Zuma said he would give an update on Mr Mandela’s condition when doctors issue a report.
The president’s office issued a statement on Saturday which said Mr Mandela was doing well and that there was “no cause for alarm”.
Mr Mandela needs medical attention “from time to time which is consistent with his age,” the statement added.
There is no information yet on what prompted his admission and it is unclear when Mr Mandela will be discharged from hospital.
The Associated Press reported that worshippers had gathered at the Regina Mundi Catholic church in the Soweto area of Johannesburg to pray for Mr Mandela.
The church was a centre of protests and funerals during apartheid.
Mr Mandela retired from public life in 2004 and has been rarely seen in public since.
He served as South Africa’s first black president between 1994 and 1999, and received the Nobel Peace Prize in 1993.
That was after spending more than two decades in jail under the white minority apartheid regime.
Mr Mandela was last in hospital in February, when he underwent a minor procedure to treat an abdominal problem.
And in January 2011 he was treated for a serious chest infection.
Mr Mandela spends the majority of his time in the rural village of Qunu, which is close to where he was born.
BBC correspondent Andrew Harding said he is known to be frail and his memory is fading, but visitors have repeatedly said he is in good spirits.