A file photograph of Nelson Mandela in 2002.
President Zuma appeared on state television on Tuesday to reassure an uneasy nation that Nelson Mandela, although in a serious condition, is receiving the best of care.
In a brief recorded interview Zuma reiterated that the anti-apartheid icon was in a stable condition.
"We are all feeling it, that our president, the real father of democracy in South Africa is in the hospital," Zuma, looking relaxed and clad in a sweater, told the South African Broadcasting Corporation.
"We need him to be with us and I'm sure that all the messages that have been pouring in to wish him a quick, speedy recovery, they are highly welcome," Zuma said.
"But that also indicates the love of our people to him and we certainly join everyone to say he should recover quickly."
"And I'm sure, knowing him as I do, he's a good fighter and he'll be with us very soon."
Mandela was rushed to hospital in the early hours of Saturday, to receive treatment for a lung infection.
Zuma meets doctors
"Yesterday [Monday] I met the team of doctors who are treating him. They gave me a very thorough briefing and really I was very confident that they know what they are doing and they're doing a very good job," Zuma said.
"Whilst it is very serious but he's stabilised and we are all praying for him really to recuperate quickly."
Meanwhile, after speculation, the presidency denied that Zuma would be visiting Mandela in hospital on Tuesday. "The president is in Cape Town preparing for the budget vote of the presidency," the statement said.
Two of Mandela's daughters arrived at the hospital in Pretoria earlier on Tuesday.
Makaziwe Mandela's red Range Rover drove past numerous police officers deployed at the hospital's entrance. Her car was followed by that of Zenani Mandela, the South African ambassador to Argentina. Unlike other cars entering the hospital, their vehicles were not searched.
Police were stationed outside the hospital, in the Pretoria suburb of Arcadia. Security at the facility had been tightened, with police officers manning the two entrances.
Police spokesperson Brigadier Phuti Setati earlier said police stationed at the hospital were part of the presidential protection services team, whose task includes protecting former presidents.
He did not specifically confirm that Mandela was in the hospital.
'Unchanged'
On Monday, the presidency said Mandela's condition was "unchanged" from Saturday and that he was receiving intensive care.
"President Jacob Zuma reiterates his call for South Africa to pray for Madiba and the family during this time," spokesperson Mac Maharaj said at the time.
Barricades were erected at the spot where journalists had been camping on Monday, forcing the press to move across the street. Police tape was used to cordon off the area.
This was the third time this year the Nobel Peace Prize laureate had been in hospital. At the end of March and in April this year 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. – AFP; Sapa