Nelson Mandela was discharged from hospital Friday after a doctor said he had "responded very well" to treatment for a lung infection.
Deputy President Kgalema Motlanthe, speaking at a press conference, repeated previous assurances, saying there was "no need for us to panic."
"There is no need for us to fear for Madiba's (Mandela's) health. He is in good health," Motlanthe said.
South Africa's surgeon-general, Vijay Ramlakan, confirmed Mandela, 92, had undergone "a few specialist investigations" after being admitted to hospital earlier this week.
He said the tests were considered "routine" for a patient with Mandela's profile.
"He recently developed an acute respiratory infection for which he received treatment and he's responded very well," Ramlakan said.
The doctor said Mandela was "stable" and "will be monitored closely." He told the press conference that Mandela would be released from hospital and cared for at home and minutes later it was confirmed he had been discharged.
Ramlakan said Mandela's "amazing, positive attitude allows him to cope with the difficulties of old age with the greatest of graces."
Mandela was admitted to hospital on Wednesday, prompting an outbreak of speculation and fears for the health of anti-apartheid icon who led South Africa as its first black president and is revered at home and abroad as a symbol of reconciliation and hope.
On Thursday, a source said Mandela had suffered a collapsed lung.
Previously, Motlanthe said Mandela was in good spirits and given his age and medical history, the tests were needed to ensure he got the best care.
"Medically there is no need to panic. Dr. Mandela suffers from (an) ailment common to people of his age, and conditions that have developed over years. We may recall that he has suffered from tuberculosis whilst on Robben Island and has had previous respiratory infections," Motlanthe said.
Mandela was diagnosed with tuberculosis in the 1980s while he was jailed and later had an operation to repair damage to his eyes. In 2001 he had treatment for prostate cancer. He was released from prison in 1990 after 27 years imprisonment.
President Jacob Zuma and the ruling African National Congress also appealed for calm.
Mandela has not been seen in public since the soccer World Cup final in July last year, when he made a brief appearance waving from a golf cart.
According to the University of Maryland Medical Center, a collapsed lung, pneumothorax, is "the collection of air in the space around the lungs", making it more difficult to breathe.
It is not life threatening and treatment can vary from allowing the body to repair the problem on its own to placing a tube in the chest to relieve the pressure.
Several members of Mandela's family, including his wife Graca Machel, visited the hospital after his admission. The White House said President Barack Obama's thoughts were with Mandela.
Mandela retired from public life in June 2004 before his 86th birthday, telling his compatriots: "Don't call me, I'll call you."