South Africa continues to pray for Nelson Mandela's health and well-being as the 94-year-old remains critically ill in hospital, the nation's president said.
Mr Zuma called Mr Mandela the "founding president of our democracy who is much loved by our people and the world".
The South African government has said Mr Mandela's condition is stable but remains critical. He was admitted to a Pretoria hospital three weeks ago with a recurring lung infection.
Mr Obama plans to make a private visit to relatives of Mr Mandela later but does not intend to see the man he has called a "personal hero".
Mr Mandela became South Africa's first democratically elected president in 1994 after spending 27 years in prison.