President Jacob Zuma said Thursday the 94-year-old former president's condition had improved, but was still critical, the BBC reported.
"He is much better today than he was when I saw him last night," Zuma said after speaking to Mandela's medical team at a Pretoria hospital, where he has been treated for a lung infection for nearly three weeks.
As crowds prayed and sang at Mandela's former home and outside the hospital Thursday, South Africa's ruling African National Congress said it would conduct vigils each day he remained hospitalized.
After visiting her grandfather Wednesday, Ndileka Mandela thanked everyone for their well-wishes.
"He's stable and we'd like to say that we thank everybody for giving their support and praying with us ... we are anxious, as you know, that he is critical but he's in a stable condition right now," she said. "It's been hard, especially because of all of this -- that we have to do everything in the public eye."
Mandela's daughter, Makaziwe Mandela, said he was "still there" and responded to touch.
"I won't lie," she said. "It doesn't look good."
Concerns were raised further Wednesday, when Zuma canceled a trip to Mozambique and visited Mandela in the hospital for the second time in just over 12 hours, The New York Times reported.
Worries over Mandela's condition overshadowed U.S. President Obama's visit Friday to South Africa as part of his African tour.
Mandela, who was imprisoned for 27 years, is venerated for leading the fight against white minority rule in South Africa and then advocating reconciliation. He received the Nobel Peace Prize in 1993 and was elected president the following year. He left office in 1999 after one term.