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Zuma, who visited Mandela on Christmas Day, said in a statement that doctors were happy with the progress the elder statesman was making.
"We found him in good spirits. He was happy to have visitors on this special day and is looking much better. The doctors are happy with the progress that he is making," said Zuma.
The 94-year-old Nobel Peace laureate has been in hospital in Pretoria for more than two weeks after being admitted for routine tests and then undergoing surgery to remove gallstones.
Zuma, who has just been re-elected as president of the ruling African National Congress party, last week described Mandela's condition as serious. Periodic statements from the presidency continue to stress that the veteran politician is responding to treatment.
No date has been given for his release from hospital. Mandela, who is internationally admired for his struggle against minority white rule, retired from public life in 2004 after serving one term as South Africa's first black president.