The anti-apartheid leader and Nobel Peace laureate was spending his fourth day in a hospital in the South African capital Pretoria yesterday.
He remains a hero to many of South Africa's 52 million people and two brief stretches in hospital in the past two years made front-page news.
"Doctors have concluded the tests, and these have revealed a recurrence of a previous lung infection, for which Madiba is receiving appropriate treatment, and he is responding to the treatment," the government said in a statement.
Mandela, whose clan name is "Madiba", was admitted to the Pretoria military hospital on Saturday after being flown from his home village of Qunu, which is in a remote, rural part of the Eastern Cape province.
Until now, South African authorities had given few details about the reason for his latest visit to hospital.
In an interview late on Monday with a South African television channel, Mandela's Mozambican-born wife Graca said the former president's "sparkle" was fading.
When he was admitted to hospital on Saturday, 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, South Africa's first black president, spent 27 years in apartheid prisons, including 18 years on Robben Island off the coast of Cape Town.