The South African president says former leader Nelson Mandela is responding to treatment at his home, where a team of doctors is caring for him.
Authorities have previously described Mandela's condition as critical.
The 95-year-old former president and leader of the anti-apartheid movement was discharged from a hospital on September 1, nearly three months after he was admitted for a recurring lung infection.
The South African Press Association quotes President Jacob Zuma as saying in a speech released on Wednesday that Mandela continues to respond to treatment.
The speech was prepared for delivery at the United Nations General Assembly in New York.
Mandela's grandson Mbuso Mandela told The New Age newspaper his grandfather was "sitting up and looking around" and had spent the Tuesday public holiday surrounded by family.
"I saw him again yesterday (Wednesday) at lunch. He is doing well," he said, adding that "we are keeping him company".
He stressed that Mandela was "much better" and not completely bed-ridden.
Mandela spent 27 years in prison during white minority rule.
He led South Africa through a delicate transition to all-race elections that propelled him to the presidency in 1994.
