Zuma said the whole nation was behind Mandela during this difficult time.
"Knowledge of the love and support of his people keeps him strong. Therefore, we urge all South Africans to keep Tata (Mandela's nickname) uppermost in their thoughts at every place of worship or entertainment tomorrow on Christmas Day, and throughout the festive season," Xinhua quoted Zuma as saying in a statement.
"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.
Zuma wished the Mandela family strength and assured them of the support of the government and the people of South Africa.
This is Mandela's longest stay in a hospital since 2001, when he underwent seven weeks of radiotherapy after being diagnosed with prostate cancer.
In an earlier update, Zuma said Mandela's health condition was "serious" but he was "responding well to treatment" and had steadily improved in the last few days after suffering a lung infection and undergoing surgery for gallstones.
Mandela has been in a Pretoria hospital since Dec 8. He underwent a successful surgery to have the gallstones removed after doctors attended to his lung infection.
Mandela, who was imprisoned for 27 years during the apartheid, became the country's first black president in 1994.
