Mr Mandela is spending his 10th day in a hospital in Pretoria, being treated for a recurring lung infection.
President Jacob Zuma said on Sunday that Mr Mandela remains in a serious condition but that his doctors are seeing sustained improvements. He added that Mr Mandela is engaging with family during visits.
In a written message, Graca Machel, Mr Mandela's wife, expressed the family's gratitude for messages of support, in particular from children singing outside the Mandela home.
The leader of South Africa's anti-apartheid movement, Mr Mandela spent 27 years in prison during white racist rule. He was freed in 1990 and became South Africa's first black president in 1994.