Mr Zuma made the comments while renaming an airport in Bloemfontein.
Mr Zuma said Mr Mandela "is recuperating from a lung infection at a Pretoria hospital. We wish him a speedy recovery and assure him yet again, of the love and support of many in the country and abroad."
Mr Mandela is 94 years old and was admitted to hospital on Saturday.
He is revered for being a leader of the struggle against racist white rule in South Africa and for preaching reconciliation once he emerged from prison in 1990 after 27 years.
He served one five-year term as president before retiring from public life.