The comment by Mandla Mandela was the latest indication that the health of his 94-year-old grandfather, South Africa's first black president, was showing signs of improvement. Mandela has been receiving visits from family members after he was rushed to hospital a week ago with a recurrence of lung problems.
"Madiba is recovering very well and looks good," Mandla Mandela said in Qunu, a village in the Eastern Cape province where Mandela was born and spent his early years.
Speaking in Xhosa at a funeral of another relative, Mandla used the clan name 'Madiba' by which Mandela is popularly known.
"I thank the nation and the world for the prayers for Madiba, and the doctors and the office of the ANC for keeping the family updated," he said.
South Africa's government said on Thursday that Mandela was continuing to recover but his condition remained serious.
Mandela's hospitalization is his fourth since December and has reinforced growing awareness among South Africa's 53 million people that they will one day have to say goodbye to the father of the "Rainbow Nation" created from the ashes of apartheid.
Mandela has a history of lung problems dating back to his time at the windswept Robben Island prison camp near Cape Town. He was released in 1990 after 27 years behind bars and went on to serve as president from 1994 to 1999.