The 94-year-old revered statesman was admitted at a Pretoria hospital, for the fourth time since December, last Saturday after suffering from a recurrent lung infection.
Two of his daughters Makaziwe and Zindzi, and former wife Winnie Madikizela-Mandela yesterday visited the hospital where the former president is staying.
Speaking to the national broadcaster SABC, Zuma said he had been updated by doctors on the health of Mandela, whose health condition is "very serious, but stable".
"We are all praying for him really to recuperate quickly," Zuma said while describing Mandela as "the father of democracy in South Africa".
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Security was tightened around the Pretoria hospital with police manning the two entrances at the the Mediclinic Heart Hospital.
Mandela had a long history of lung problems, dating back to the time when he was a political prisoner on Robben Island during apartheid. He contracted tuberculosis in 1988 during his 27 years in prison.
Mandela, one of the world's tallest statesmen, led the movement to replace the apartheid regime of South Africa with a multi-racial democracy.
Mandela served as South Africa's first black president from 1994 to 1999. He won the Nobel Peace Prize in 1993.