Presidential spokesman Mac Maharaj said the physicians caring for Mr Mandela had given no indication of an "imminent discharge" from a hospital in Pretoria, the capital, according to IOL, a South African news website.
Mandela was went into hospital on December 8. He was diagnosed with a lung infection and also had gallstone surgery.
Officials said his condition has improved and that he was responding to treatment.
President Jacob Zuma acknowledged several days ago that Mr Mandela's condition had been serious.
South African Archbishop Desmond Tutu said he is praying for a prompt recovery for Mr Mandela.
Radio 702, a South African station, broadcast an interview with Mr Tutu in which he said he exchanged text messages about Mr Mandela with the anti-apartheid icon's wife, Graca Machel.
Mr Tutu and Mr Mandela are Nobel laureates because of their role in the struggle against white minority rule.
Mr Mandela was imprisoned for 27 years and served one five-year term as president after he was elected in South Africa's first democratic elections in 1994.