Mandela, 94, had been ill for some days before being transferred in the early hours of Saturday to a hospital in Pretoria.
It is the third time this year he has been admitted to hospital.  The BBC's Karen Allen in Pretoria says there is a sense of calm across South Africa, and also a quiet hope that the man who led the fight against apartheid may regain his strength once again.
Mandela's wife, Graca Machel, cancelled a scheduled appearance in London to remain at her husband's bedside.