"Former President Mandela is still in a critical condition in hospital but shows sustained improvement," President Jacob Zuma said in a statement.
Mandela, who turned 95 on July 18, was admitted to a Pretoria hospital on June 8. He has been hospitalised four times since December.
Mandela, South Africa's first black president, is regarded the founding father of the country's multi-racial democracy.
Mandela had a long history of lung problems, dating back to the time when he was a political prisoner on Robben Island during apartheid. While in jail he contracted tuberculosis.
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He served as the country's president from 1994 to 1999. He left power after five years as president.
Mandela, respected across the globe as a symbol of resistance against injustice, was awarded the Nobel Peace Prize in 1993.
He retired from public life in 2004 and has not been seen in public since the football World Cup final in 2010.