Mr Zuma said he had visited Mandela and "was informed by the medical team that Madiba's condition has improved during the course of the night".
"He remains critical but is now stable," Zuma said.
Mr Zuma last night cancelled a scheduled trip to Mozambique, where he was due to visit today to attend the SADC Regional Summit on Infrastructure Investment.
"I cancelled my visit to Mozambique today so that I could see him and confer with the doctors. He is much better today than he was when I saw him last night. The medical team continues to do a sterling job. We must pray for Tata's health and wish him well. We must also continue with our work and daily activities while Madiba remains hospitalised," President Zuma said.
Zuma said he was "disturbed by the rumours that are being spread about former President Mandela's health" and appealed for "for respect for the privacy and dignity of the former President".
Mr Mandela, known by his clan name Madiba, was taken to hospital in Pretoria on June 4 for the third time this year, with a lung infection.
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