"Doctors attending to former President Mandela have reported that he has made progress during the past 24 hours and they are satisfied with the way he is responding to treatment," President Jacob Zuma's office said a statement.
South Africa's first black president, who came to power in historic all-race elections in 1994, remains a hero to many of its 52 million people.
Mandela, known locally by his clan name of 'Madiba', was admitted to Pretoria's '1 Military' Hospital on Saturday after being flown from his home village of Qunu in a remote, rural part of the Eastern Cape province.
The government only gave the first concrete details about his condition on Tuesday, saying he had suffered a recurrence of a lung infection.
When he was admitted, officials stressed there was no cause for concern although domestic media reports suggested senior members of the government and people close to him had been caught unawares.
Mandela, a global symbol of resistance to racism and injustice, spent 27 years in apartheid prisons, including 18 years on the windswept Robben Island off the coast of Cape Town.
He was released in 1990 and went on to use his unparalleled prestige to push for reconciliation between whites and blacks as the bedrock of the post-apartheid "Rainbow Nation".
He stepped down in 1999 after one term in office and has been largely removed from public life for the last decade.
Mandela spent time in a Johannesburg hospital in 2011 with a respiratory condition, and again in February this year because of abdominal pains. He was released the following day after a keyhole examination showed there was nothing serious.
He has since spent most of his time in Qunu.
His fragile health prevents him from making any public appearances in South Africa, although he has continued to receive high-profile domestic and international visitors, including former U.S. President Bill Clinton in July.