Speaking in the National Assembly on Wednesday, Zuma said: "We are happy to report that former president Nelson Mandela is responding to treatment. We are happy with the progress he is making during these difficult days. We appreciate the support from the international community. We are proud to call him our own. We ask you to continue to keep him in your thoughts and prayers."
Meanwhile, Tibet's exiled spiritual leader the Dalai Lama said on Wednesday he was "one of the greatest admirers" of Mandela and pledged to perpetuate his ideals.
Speaking to France Info radio while in New Zealand, the Dalai Lama said South Africa's anti-apartheid icons like Mandela and Desmond Tutu were ageing and frail and "logically they are going to go".
"The important thing is to preserve his memory," the Dalai Lama said. "Nelson Mandela is very ill, Desmond Tutu also quite old … [The] important thing is their teaching, their spirit must carry."
"I feel it is my responsibility" to ensure that and to see they inspire even after they have gone, the Tibetan leader added.
Under apartheid, Tutu campaigned against white minority rule and was awarded the 1984 Nobel Peace Prize. The Dalai Lama (77) won the Nobel Peace Prize in 1989. Mandela was awarded the honour in 1993 jointly with FW De Klerk, South Africa's last apartheid-era president.
Family visits
Mandela's eldest daughter Zenani Mandela-Dlamini arrived at the Pretoria hospital on Wednesday where the elderly statesman is believed to be receiving treatment.
Her black Mercedes-Benz entered the Medi-Clinic Heart Hospital before 11am. She stopped briefly and talked to police officers at the entrance on Park Street in Arcadia.
Mandela-Dlamini, who is South Africa's ambassador to Argentina, arrived home this week following her father's admission.
Mandela's wife Graça Machel and his grandson Mandla also arrived at the hospital on Wednesday.
Photographers rushed into the busy Park Street in Arcadia as a Mercedes-Benz ferrying Machel, followed by Mandla's black Toyota Land Cruiser entered the premises.
Another grandson, Ndaba, was at the hospital earlier in the day.
She came home this week following her father's admission. The ailing icon was spending his fifth day in hospital.
Hospital admission
On Saturday, the presidency announced Mandela had been admitted to hospital in the early hours of the morning and was in a "serious but stable" condition.
His condition had remained unchanged since then.The presidency said on Tuesday that the doctors treating Mandela gave President Jacob Zuma a thorough briefing on Monday night.
"President Zuma has full confidence in the medical team, and is satisfied that they are doing their best to make Madiba better," spokesperson Mac Maharaj said in a statement.
Police had taken over security at the hospital. Seven officers were guarding the facility's entrance. Pedestrians' bags and vehicles entering the premises were searched.
Local and international media continued to hold vigil outside the hospital and Mandela's Houghton, Johannesburg, home.
This is the third time this year the Nobel Peace Prize laureate has been hospitalised. At the end of March he spent nine days in hospital receiving treatment for recurring lung problems.
Earlier in March he was admitted to a Pretoria hospital for a scheduled check-up and discharged the following day. – Sapa