The 94-year-old Nobel Peace laureate and South Africa's first black post-apartheid president, was admitted to a Pretoria hospital on December 8.
He has been treated there for a recurrent lung infection and had surgery to remove gallstones.
In a statement, president Jacob Zuma said his predecessor "continues to respond to treatment".
"Knowledge of the love and support of his people keeps him strong," Mr Zuma said.
"We urge all South Africans to keep Tata (father) 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."
There was no indication of when he might be discharged.
Only limited details of Mr Mandela's condition have been made public by the South African government, which has repeatedly called on the public to respect the former president's privacy.
Before his retirement in 2004, Mr Mandela used to host a Christmas feast in his home village of Qunu for impoverished children.
Since retiring from public life, Christmas has been a more low-key affair, spent with family.
Neither tradition will be repeated this year.
Meanwhile, former British prime minister Margaret Thatcher has spent a fifth day in hospital as she recovers from bladder surgery.
There was no change in Baroness Thatcher's condition a day earlier when the 87-year-old was said to be "in good spirits", a spokeswoman said.
The former premier was admitted to hospital last week for a minor operation to remove a growth in her bladder after suffering pain earlier in the week.
The former Conservative Party leader was Britain's prime minister from 1979 to 1990 and remains the only woman premier in British history.