Zindzi Mandela said her father was now able to sit up for several minutes in his bed.
The 95-year-old has been in a Pretoria hospital for two months for treatment of a recurrent lung infection.
The government said late last month his condition remained critical but was showing improvement.
Speaking to state-owned public broadcaster SABC, Zindzi Mandela – who uses the Xhosa word for father “Tata” – said: “He’s fine. Tata now manages to sit up, like now he sits up in a chair for a few minutes in a day.
“Every day you know he becomes more alert and responsive. Tata is determined not to go anywhere anytime soon, I cannot stress this enough.”
She said her father has a strong constitution, will and strength which keeps him alive.
Zindzi Mandela added: “He just doesn’t have the strength of a man, he has the strength that is beyond anything that can be explained. Even now with the challenges to his health, he somehow manages to bounce back when everyone assumes this is the end.”
Her comments come after Mandela’s ex-wife Winnie Madikizela-Mandela told how the former president was now breathing normally.
Madikizela-Mandela had denied reports Mandela was in a permanent vegetative state, saying there was no need to conceal the fact.
She described how his eyes still “lit up” when his children came to visit him. “That is how he communicates with them,” she said.
And she praised the health team in Pretoria who are treating the 95-year-old, saying they were doing all they could to ensure he remained “comfortable.”
Well-wishers continue to place cards, flowers and balloons at the hospital entrance that has become a shrine adorned with flags and paintings. Mandela was admitted to the Pretoria hospital with a recurring lung infection on 8 June, and has remained in doctor’s care ever since.
There were mixed reports about the state of the former leader’s health with some sources claiming he was being kept alive on a life support machine.
But his family has said he has always been conscious and aware of what is going on.
President Jacob Zuma’s office last week said the global icon was in a stable condition and called for the nation to continue praying for Mandela.
Mandela’s ongoing lung condition is understood to be linked to the many years he spent in captivity on Robben Island.
The former statesman is revered across the world for his role in ending apartheid in South Africa.