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The revered anti-apartheid leader and Nobel Peace laureate is spending his fourth day in hospital in the capital, Pretoria.
Known affectionately by his clan name "Madiba", Mandela 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 was admitted to the Pretoria military hospital on Saturday after being flown from his home village of Qunu in a remote part of the Eastern Cape province.
Until now, authorities had given few details about the reason for his latest visit to hospital.
In an interview broadcast on South Africa's eNCA 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.
On the streets, ordinary South Africans crossed their fingers for his recovery. Leading cartoonist Zapiro depicted Mandela asleep in his hospital bed with hundreds of "Get Well" cards flying through the window like a flock of birds.
"He's old and I hope he gets better soon. He means a lot to the world," 25-year-old legal researcher Liezel Jacobs said.
Mandela, South Africa's first black president and 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 be elected president in the historic all-race elections in 1994 that ended decades of white-minority rule in Africa's most important economy.
He used his unparalleled prestige to push for reconciliation between whites and blacks, setting up a commission to probe crimes committed by both sides in the anti-apartheid struggle.
Mandela's African National Congress (ANC) has continued to govern since his retirement from politics in 1999, but has been criticised for perceived corruption and slowness in addressing apartheid-era inequalities in housing, education and healthcare.
On Tuesday, the influential South African Council of Churches launched a blistering attack on the ANC, accusing its leaders of moral decay and of abandoning Mandela's goal of a non-racial democracy built from the ashes of apartheid.
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, although he has continued to receive high-profile domestic and international visitors, including former U.S. President Bill Clinton in July.