The president has been reassured that Mandela is in the hands of a competent medical team at the hospital in Pretoria, Mac Maharaj, presidential spokesperson said.
94-year-old Mandela, who was South Africa's first black President, was hospitalised yesterday "to undergo tests," President Jacob Zuma's office had said in a statement.
The Nobel peace prize laureate "is doing well and there is no cause for alarm," the statement said.
Local media reports said that the decision to move him was taken so quickly, some family members and his own foundation were initially unaware it had happened.
South Africans had been waiting for word on Mandela's condition amid messages of hope for a speedy recovery.
Prayers were held for the former leader at the Regina Mundi Catholic church in the Soweto area of Johannesburg, once the centre of protests and funerals during apartheid.
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"As said before, former President Mandela will receive medical attention from time to time which is consistent with his age," Mac Maharaj was quoted as saying by News24.
In January 2011, Mandela was treated for a serious chest infection. A year later, he underwent a diagnostic procedure for an abdominal problem.
Mandela spent over two decades in prison under the white minority apartheid regime.
Mandela retired from public life in 2004 and has been rarely seen in public since.
He served as South Africa's first black president between 1994 and 1999, and received the Nobel Peace Prize in 1993.