The Presidency said in a statement today that former president Nelson Mandela's doctors have concluded their 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".
"President Zuma thanks the public for continuous support to former President Mandela and his family at this time."
Madiba, who has not made a public appearance since the 2010 Fifa Soccer World Cup, is known to have contracted tuberculosis during his years in prison.
He also had a respiratory infection in 2011.
Mandela, 94, was reported to have been admitted to One Military Hospital in Pretoria on Saturday.
On Sunday morning, President Zuma visited Mandela in hospital and found him "comfortable, and in good care", his spokesman Mac Maharaj said.
Defence Minister Nosiviwe Mapisa-Nqakula reportedly also visited Mandela on Monday.According to the Associated Press, she said Mandela was "doing very, very well".