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. He then underwent surgery to remove gallstones.
Mandela, who came to power in historic elections in 1994 after decades struggling against apartheid, remains a symbol of resistance to racism and injustice at home and around the world.
He has a history of lung problems dating back to when he contracted tuberculosis while in jail as a political prisoner. But this is his longest stay in hospital since he was released from prison in 1990.
He spent time in a Johannesburg hospital in 2011 with a respiratory condition, and again in February this year because of abdominal pains though he was released the following day after a keyhole examination showed there was nothing serious.
Zuma, who has just been re-elected as president of the ruling African National Congress party, last week described Mandela's condition as serious.
"The Mandela family truly appreciates all the support they are receiving from the public. That is what keeps them going at this difficult time," said Zuma.
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 spent 27 years in prison, including 18 years on the windswept Robben Island off Cape Town.
After his release, he used his popularity to push for reconciliation between whites and blacks. This reconciliation is the bedrock of the post-apartheid "Rainbow Nation".
Sworn in as South Africa's first black president in 1994, Mandela stepped down in 1999 after one term in office and has largely been absent from public life for the last decade.
His fragile health has prevented him from making any public appearances in South Africa, though he has continued to receive high-profile domestic and international visitors, including former U.S. president Bill Clinton in July.