JOHANNESBURG — After a second night in a hospital being treated for a recurrent lung infection, former President Nelson Mandela of South Africa was in good spirits on Friday, enjoying breakfast and making steady progress, according to the office of President Jacob Zuma, who had earlier urged his compatriots not to panic.

But the statement from Mr. Zuma gave no clue about when Mr. Mandela, 94, might be discharged. He was admitted to the hospital late Wednesday night for the third time in four months. The authorities delayed an initial announcement for several hours, and the episode has rekindled worries about his frailty.

In its latest statement on Friday Mr. Zuma’s office said: “The presidency wishes to advise that former President Nelson Mandela is in good spirits and enjoyed a full breakfast this morning, 29 March 2013. The doctors report that he is making steady progress. He remains under treatment and observation in hospital.”

The brief bulletin, which did not explain the details of Mr. Mandela’s condition, came hours after Mr. Zuma seemed to be seeking to steady South African public opinion, urging his compatriots to “slow down the anxiety” but counseling them to think about the former president’s advancing years.