The anti-apartheid leader remains in serious but stable condition in a hospital, the office of President Jacob Zuma said in a statement.
The government confirmed reports about transport problems when the former leader was taken to the hospital for what officials have said is a recurring lung infection. CBS News reported that Mandela had to be transferred in wintertime temperatures to another ambulance in the early morning of June 8 after waiting on the side of the highway for 40 minutes.
The government said doctors are satisfied that the Nobel Peace Prize laureate suffered "no harm" at the time.
Mandela was taken from his home in the Johannesburg neighborhood of Houghton to a hospital in Pretoria, the capital, about 31 miles away.
"The fully equipped military ICU ambulance had a full complement of specialist medical staff including intensive care specialists and ICU nurses. The convoy also included two quick response vehicles," the presidency said. "When the ambulance experienced engine problems it was decided that it would be best to transfer to another military ambulance which itself was accompanied for the rest of the journey by a civilian ambulance."
The statement added: "All care was taken to ensure that the former president Mandela's medical condition was not compromised by the unforeseen incident."
In recent days, reports from the government, former President Thabo Mbeki and a grandson of Mandela have indicated that the health of Mandela is improving, although he has been in the hospital for treatment several times in recent months.
Close family members have been visiting him daily in a Pretoria hospital amid an outpouring of prayers and messages of support from South Africans and people around the world.
Zuma's office appealed for Mandela's privacy to be respected "and that he be accorded the doctor-patient confidentiality that all patients are entitled to in terms of medical ethics."
Mandela was jailed for 27 years under white racist rule and was released in 1990. He then played a leading role in steering the divided country from the apartheid era to democracy, becoming South Africa's first black president in all-race elections in 1994. As a result of his sacrifice and peacemaking efforts, he is seen by many around the world as a symbol of reconciliation.