The former president first contracted tuberculosis in the 1980s while detained on windswept Robben Island.
His lungs are said to have been damaged while working in a prison quarry. This latest spell in hospital is his fourth in just over two years.
Mr Mandela served as South Africa’s first black president from 1994 to 1999 and is regarded by many as the father of the nation for leading the struggle against apartheid.
The statement issued by President Zuma’s office on Friday said: “Former President Nelson Mandela is in good spirits and enjoyed a full breakfast this morning. The doctors report that he is making steady progress.”
Mr Mandela remains under treatment in hospital.
Last December he was treated for a lung infection and gallstones – his longest period in hospital since leaving prison in 1990. In February, he was treated for a stomach condition.
On Thursday, US President Barack Obama said he was “deeply concerned with Nelson Mandela’s health”, adding that “we will be keeping him in our thoughts and prayers”.
Earlier, when asked whether people should prepare for the inevitable, Mr Zuma said: “In Zulu, when someone passes away who is very old, people say he or she has gone home. I think those are some of the things we should be thinking about.”
But he stressed that Mr Mandela had been able to handle the situation “very well” so far.
“Very few outstanding personalities in the world live to his level,” he said.
Mr Mandela retired from public life in 2004 and has been rarely seen in public since.
Despite his long imprisonment, Mr Mandela forgave his former enemies and as president urged South Africans of all races to work together and seek reconciliation.
In 1993 he was awarded the Nobel Peace Prize.
His main home is in Qunu, a small rural village in Eastern Cape province, where he says he spent the happiest days of his childhood.
However, doctors said in December he should remain at his home in the Johannesburg neighbourhood of Houghton to be close to medical facilities.
Reprinted from BBCnews