"Tata (father) now manages to sit up, like now he is able to sit up in a chair for a few minutes in a day. Everyday you know, he becomes more alert, more responsive, and so on," Zindzi Mandela told South Africa public television SABC on Friday.
"Tata is determined not to go anywhere anytime soon, I cannot stress this enough.
The former South African president was rushed to the Mediclinic Heart Hospital on June 8 with a recurring lung infection.
His condition is still said to be "critical but stable".
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But the last two months have seen a series of scares for the Nobel Peace Prize laureate and for the country where he is considered a living saint.
On June 23 the presidency said his "condition had become critical over the past 24 hours," as President Jacob Zuma cancelled a foreign trip.
But since then friends and family members reported the peace icon's health was improving, with his former wife Winnie Madikizela-Mandela telling Sky News in an interview broadcast Thursday that the 95-year-old was "now breathing normally".
"You know he just doesn't have the strength of a man, he just has a strength that is beyond anything that can be explained," said Zindzi.
"Because even now with the challenges to his health, he somehow manages to bounce back when everyone assumes this is the end.