Nelson Mandela's condition has improved and he "remains critical but is now stable", South African officials said on Thursday.
President Jacob Zuma visited Mandela in hospital in Pretoria after abandoning a planned trip to a summit in Mozambique. Mandela's medical team advised him of a slight improvement in the former president's health.
"I cancelled my visit to Mozambique today so that I can see him and confer with the doctors," Zuma said. "He is much better today than he was when I saw him last night. The medical team continues to do a sterling job. We must pray for Tata's health and wish him well. We must also continue with our work and daily activities while Madiba remains hospitalised."
The presidency added that it was disturbed by rumours being spread about Mandela's health and appealed for his privacy to be respected.
Mandela's eldest daughter has given a rare insight into his condition and accused foreign journalists of behaving like vultures.
Makaziwe Mandela said Zuma's decision to scrap his travel plans showed that "anything is imminent. I can also state that God only knows when it is the time to go."
In an interview with the public broadcaster SABC she said Mandela was still opening his eyes and still reactive to touch.
"We will live with hope until the final end comes. I don't want to lie. He doesn't look good. But he's still opening his eyes. He might be waning off but he's still there. I think for us as his children and grandchildren, as long as he's still there we want to give him the positive support, the positive energy."
Makaziwe vented family frustration at the intense media scrutiny that has followed their every move. "There is sort of a racist element with the foreign media, where they just cross boundaries," she said.
"You have no idea what is happening at the hospital. In the middle of Park Street they just stand. You can't even get into the hospital. Truly, like vultures, it is like they are waiting for the last carcasses. That is what we feel as a family."
It was understandable that journalists were interested in Mandela's health, she added, "but they are going overboard".
She contrasted the situation with the death of Margaret Thatcher earlier this year. "Is it just because we're an African country that they feel they don't have to respect this? I just think it's crass. If people think they really care about Nelson Mandela they should respect that. Part of him should be respected, not everything of him should be out in the public."
Zuma visited Mandela at about 10pm on Wednesday and found he remained in a critical condition. Doctors "are still doing everything they can to ensure his wellbeing", the presidency said.
Officials did not deny claims that he was on a life-support machine. "Yes he is using machines to breathe," Napilisi Mandela was quoted as saying in media reports after visiting the hospital on Wednesday. "It is bad but what can we do?"
Mandela's grandchildren gathered up cards, flowers and stuffed animals outside the hospital on Thursday and took them inside. They gave thanks for the public's support.
Members of a South African Salvation Army choir prayed and sang outside the hospital and the African National Congress (ANC) youth league spoke about Mandela's achievements.
Hundreds of people from South Africa, around the continent and the world gathered at the site along with numerous international TV crews.
Mandela has already spent 20 days in the hospital with a recurring lung infection, his fourth admission in six months. Many South Africans appear to be slowly coming to terms with the prospect of losing the father of the nation.
The US president, Barack Obama, is due to arrive in South Africa on Friday as part of a three-nation Africa tour he has already started in Senegal. Officials said it was too early to say whether Obama's schedule in Johannesburg and Cape Town on Saturday and Sunday might be affected by Mandela's worsening condition.
Meanwhile an Australian politician apologised on Thursday to South Africa's high commissioner for incorrectly announcing that Mandela had died.
The resources minister, Gary Gray, acknowledged he wrongly told guests attending a dinner at Parliament House on Wednesday that the anti-apartheid leader was dead. "I apologise unreservedly and am deeply sorry to have relayed what I thought was reliable advice," Gray said.