The 94 year old is spending his sixth day in the Pretoria hospital suffering from a recurrent lung infection.
He became South Africa's first black president in 1994 after leading the struggle against white minority rule.
He stepped down five years later.
In a statement on Thursday, Mr Zuma urged South Africans to wish Mr Mandela "a speedy recovery".
The brief statement provided no further details.
Earlier, Mr Mandela's grandson and family heir, Mandla, said the family had "been deeply touched" by the concern shown for Mr Mandela's health.
Mr Mandela's wife Graca Machel has been at his bedside regularly since calling off a trip to London last week.
His daughter Zenani, who is the ambassador to Argentina, has also returned to South Africa to visit him.
Mr Mandela has been in intensive care since he was taken to hospital on Saturday for the third time this year.
In December, he spent 18 days undergoing treatment for a lung infection and gallstones.
Before being admitted to hospital, Mr Mandela had been ill for some days at his Johannesburg home, with a recurrence of his long-standing lung problems, the president's office said on Tuesday.
Mr Mandela was imprisoned for 27 years for his role in the fight against apartheid and is believed to have suffered damage to his lungs while working in a prison quarry.
He contracted tuberculosis in the 1980s while being held in jail on the windswept Robben Island.
He retired from public life in 2004 and has been rarely seen at official events since.