South African President Jacob Zuma has visited Nelson Mandela in hospital and says he "looks well after a restful night", Mr Zuma's spokesperson said.
The president has been reassured that Mr Mandela is in the hands of a competent medical team at the hospital in Pretoria, Mac Maharaj told the BBC.
The 94-year-old was admitted to hospital on Saturday to undergo tests.
South Africans have been waiting for word on Mr Mandela's condition amid messages of hope for a speedy recovery.
Mr Mandela was taken from his home in the rural village of Qunu, in Eastern Cape province, to hospital in the capital on Saturday. Local media report that the decision to move him was taken so quickly, some family members and his own foundation were initially unaware it had happened.
Mr Zuma's office said on Saturday that Mr Mandela was doing well and that 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.
The authorities are keen to respect Mr Mandela's privacy and control any information about his health, the BBC's Andrew Harding in Johannesburg reports.
But there is enormous public concern here for the man widely revered as the father of democratic South Africa, he adds.
Prayers were held for the former leader at the Regina Mundi Catholic church in the Soweto area of Johannesburg, once the centre of protests and funerals during apartheid.
"Yes, it really worries us because he is a great person," churchgoer Shainet Mnkomo told Associated Press. "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 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 Qunu, which is close to where he was born.
Our correspondent says he is known to be frail and his memory is fading, but visitors have repeatedly said he is in good spirits.