Mandela has been in the Medi-Clinic Heart Hospital in Pretoria for a week – the fourth time the 94-year-old former president has been admitted to hospital since December.
"We are grateful that he continues to get better," Zuma said. "Over the last two days, although he remains serious, his doctors have stated that his improvement has been sustained."
Zuma was addressing a gathering for Youth Day in eMadadeni in KwaZulu-Natal in remembrance of the 1976 Soweto youth uprisings against apartheid.
Zuma, accompanied by African National Congress treasurer general Zweli Mkhize, visited him on Thursday.
Mandela's repeated bouts of illness have reinforced a creeping realisation among South Africa's 53-million people that they will one day have to say goodbye to their first black president.
'Get well soon Tata'
A string of balloons with slogans such as "Get well soon Tata" were hung on the gate outside the hospital. Others have hung up posters, cards and placards, flowers, and a small South African flag.
Cards on some of the flowers read: "Dear Mr Mandela, stay strong! You are in our thoughts and prayers" and "Get well soon daddy Mandela … Happy Father's Day".
Many of the hand-drawn cards pasted on the wall outside the hospital contained colourful messages and hand prints from young children.
One read: "Nalneson Mabdela [sic]. We love you may god bless you so much".
A picture of a crying woman with blond hair had the words: "We love you Mandela. God bless you."
Updating mourners
Mandela's grandson Mandla updated mourners on his condition at the funeral of the former president's cousin, Florence Mandela, in Qunu, Eastern Cape, on Saturday.
"He is doing better," Mandla said in isiXhosa.
On Saturday, Mandela's daughter Zenani Mandela-Dlamini entered and left the hospital. Family members were expected to visit the former statesman on Father's Day and Youth Day.
Mandela's former wife Winnie Madikizela-Mandela visited him on Sunday afternoon.
Madikizela-Mandela entered the Medi-Clinic Heart Hospital in Pretoria shortly after 1pm.
Mandela's granddaughter Ndileka Mandela left the hospital shortly after 11.30am on Father's Day. Another of his granddaughters, Zaziwe, accompanied her mother carrying a basket.
Police officers at the hospital's two entrances searched each car before it entered. The number of journalists outside the hospital decreased slightly on Sunday morning compared with earlier in the week.
Camera crews were stationed at both entrances in the hope of catching family members as they entered and left the hospital.
Turned away
A delegation of Christians was turned away from Mandela's Qunu, Eastern Cape, home on Sunday because they were taking photographs after being warned not to, police said.
"They were taking some photos [outside the house] after they were informed not to take any," Lieutenant-Colonel Mzukisi Fatyela said.
Two policemen turned away the missionaries from the Reformed Church of Christ and the Apostolic Faith Mission when they arrived at the Mandela house to offer their prayers and support.
A Sapa correspondent reported that two members of the group, while attempting to take pictures of themselves outside the house, were temporarily arrested and held inside a security room at the gate. This resulted in a heated exchange between the group and the police.
"It was not a big issue, there were no arrests," Fatyela said.
Apostolic Faith Mission women's leader Nomzingisi Jonga (44) said they went to the gate wanting to know why the two were arrested.
“We came here because we had a prophecy at our night vigil yesterday [Saturday], to … pray for Madiba in his grounds. Now we are being denied access and also we were told not to pray in front of his gate.
“I wish I could share with you the prophecy but now it is only God who knows. Let his will be done,” said Jonga.
The group then crossed the N2 Transkei road, to pray in public. Thambisa Nomatshitshi (21) said she was disappointed at how the police treated them.
“You cannot just arrest us because we are praying for Mandela, it's wrong … we did nothing wrong,” she said.
One police officer accused the group of betraying the freedom Mandela fought for. – Sapa, Reuters