"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 Mr Zuma.
Former British prime minister Margaret Thatcher and former US president George HW Bush also spent the holiday in hospital.
Mr Mandela was admitted to hospital in Pretoria on December 8, where he was treated for a recurring lung infection. It was later discovered he had gallstones and he underwent a successful operation on December 15.
In the first official acknowledgment that Mr Mandela’s condition was serious, President Jacob Zuma said on Thursday that Madiba had been seriously ill but he had "steadily improved over the last few days".
Mr Zuma said on Monday the whole nation was behind Mr Mandela during this difficult period. "Knowledge of the love and support of his people keeps him strong. Therefore, we urge all South Africans to keep Tata uppermost in their thoughts at every place of worship or entertainment tomorrow on Christmas Day, and throughout the festive season. We also humbly invite all freedom loving people around the world to pray for him. He is an ardent fighter and will recover from this episode with all our support,'' he said.
Presidential spokesman Mac Maharaj said on Sunday: "We all wish that he could be home for Christmas, but first and foremost he needs to get better.
Mr Mandela used to throw lavish Christmas parties for children in his Eastern Cape rural home village of Qunu, where children from impoverished backgrounds would be showered with gifts.
American talk show host Oprah Winfrey, a close friend of Mr Mandela, attended a party in 2002.
However, the events ceased after he retired from public life in 2004 and since then he has been spending Christmas privately with his family.
The ailing anti-apartheid icon was able to enjoy last year’s Christmas with family and close friends in the comfort of his home in Qunu.
People across the country have taken to Twitter to wish Mr Mandela a speedy recovery and the opportunity to spend Christmas at home.
Lynn Hoff said: "Thinking of Madiba and wishing him a speedy recovery. Really hope he will be able to go home for Christmas so he can spend it with his family."
Mishali Parbhoo tweeted: "Get well soon #Madiba and celebrate christmas at home with your family, because we want to see you live forever #GetWellSoonMadiba."
Meanwhile, Ms Thatcher remained in hospital over Christmas.
Her spokesman said she was "in good spirits" in hospital on Sunday, as she continued her recovery from a bladder operation.
Ms Thatcher, 87, was admitted to hospital on Thursday for a minor operation to remove a growth in her bladder after suffering pain earlier in the week.
On the other side of the Atlantic, Mr Bush, 88, also spent Christmas in hospital.
The former US president has been in hospital for a month undergoing treatment for bronchitis.
With Nick Hedley, Sapa and Reuters