The 95-year-old former president and anti-apartheid icon has been in hospital for more than two months with a recurring lung infection.
"Former President Nelson Mandela continues to receive treatment in hospital in Pretoria and doctors have indicated to President Jacob Zuma that the former president is making a slow but steady improvement," a statement from the presidency said.
"The medical team also reiterated that although his health was improving steadily, Madiba still remained in a critical condition," it added, referring to Mandela by his clan name.
The South African president is technically the only person authorised to give public updates about Mandela's health, and had not issued a statement since July 31.
Mandela's youngest daughter Zindzi Mandela said on Friday that the anti-apartheid hero was "not going anywhere anytime soon" and was now able to sit up unaccompanied. He was "more alert, more responsive," she said.
And his former wife Winnie Madikizela-Mandela told Sky News on Thursday that he was "now breathing normally."
Doctors had managed to contain his lung infection but kept "draining fluid from the lungs," she said.
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