The doctors attending to Nelson Mandela reported on Wednesday that he had made progress during the past 24 hours and that they were satisfied with the way he was responding to treatment, the Presidency said in an update on the former president's health.
Mandela is being treated for a lung infection at a hospital in Pretoria, where he was admitted on Saturday in order to undergo tests.
There has been an outpouring of well wishes for Madiba from South Africans from all walks of life since news of his illness broke.
A large media contingency has been camped outside Pretoria's 1 Military Hospital, where security has been beefed up, although the Presidency has not confirmed that Mandela is being treated there.
"We continue to request that Madiba and his family be accorded the necessary space and privacy, and thank the media and the public for cooperation," the Presidency said in a statement on Wednesday.
On Tuesday, the Presidency said tests had revealed a recurrence of a previous lung infection, "for which Madiba is receiving appropriate treatment, and he is responding to the treatment".
President Jacob Zuma "thanks the public for continuous support to former President Mandela and his family at this time," the Presidency added.
Zuma visited Mandela at the hospital in Pretoria on Sunday, after which he assured South Africans that Madiba was doing well and that there was no cause for alarm.
"He found him comfortable, and in good care," the Presidency said.
Mandela, who turned 94 in July, underwent treatment for a similar respiratory infection at Johannesburg's Milpark Hospital in January 2011.
"We wish Madiba all the best," Zuma said. "The medical team is assured of our support as they look after and ensure the comfort of our beloved founding president of a free and democratic South Africa."