"The presidency has been consistent that [Mandela] is in a hospital in Pretoria and avoided identifying the precise hospital for reasons regarding the privacy for Madiba and his family," spokesperson Mac Maharaj said.
He said this was to ensure his treatment was administered in the most conducive conditions for his recovery.
"For those reasons we have avoided disclosing the precise hospital."
His comments came after a report on Eyewitness News that Mandela was not receiving treatment at One Military Hospital in Pretoria.
A large contingent of journalists from local and international media have been camping outside the One Military Hospital since Saturday.
On Monday Minister Nosiviwe Mapisa-Nqakula stopped to speak to journalists outside One Military Hospital.
"He's doing very, very well," the minister said in brief comments. "And it is important to keep him in our prayers and also to be as calm as possible and not cause a state of panic because I think that is not what all of us need."
The former president (94) was hospitalised over the weekend.
He was flown from his home in Qunu, Eastern Cape, on Saturday, to a Pretoria facility.
The presidency said he was suffering from the recurrence of a previous lung infection and was responding to treatment.
The hospital is part of the Thaba Tshwane Military Base, a national security zone.
Soldiers were manning the hospital's main entrance, using plastic cones to control the movement of vehicles. Every vehicle entering the premises was being inspected.
Mandela's current stay in the hospital has become his longest continuous period in hospital since 2001, when he underwent seven weeks of radiotherapy after being diagnosed with prostate cancer. He was 83 at the time.
In January 2011, Mandela was admitted to a Johannesburg hospital for what turned out to be an acute respiratory infection.
He had contracted tuberculosis while in prison.
Mandela is revered for being a leader of the struggle against racist white rule in South Africa, and for preaching reconciliation once he emerged from prison in 1990, after 27 years behind bars.
He served one five-year term as president before retiring from public life. – Sapa