It was the day the pressure became too much to bear. As Nelson Mandela clung to life in hospital and hundreds of people gathered to pray for a miracle recovery, his family lashed out at the foreign media for "a racist element" and behaving like "vultures".

Thursday began with knife-edge anxiety over the 94-year-old's deteriorating health and concern about what news the day would bring. After visiting him in hospital in Pretoria, South African president Jacob Zuma reported that Mandela was "much better" than the night before and "remains critical but is now stable".

Every such statement, along with countless rumours and tweets, only adds to the jumpiness of media organisations seeking any scrap of information. The anti-apartheid hero's relatives in particular have come under intense scrutiny.

On Thursday the situation reached boiling point as his eldest daughter Makaziwe, who has emerged as the senior member of the Mandela family, launched an emotional attack.

"There's sort of a racist element with many of the foreign media, where they just cross boundaries," she told the national public broadcaster SABC.

"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. It's like truly vultures waiting when a lion has devoured a buffalo, waiting there for the last carcasses. That's the image that we have, as a family."

It is understandable that journalists are interested in Mandela's health, she added, "but they are going overboard".

Makaziwe 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."

Makaziwe and other family members are regularly filmed as they visit the hospital on a daily basis. When Makaziwe called a family meeting in Mandela's ancestral home of Qunu on Tuesday, its content was the subject of wildly conflicting reports. Recently Makaziwe has been the subject of unwanted headlines .

Mandela's eldest grandchild Ndileka Mandela, who was at the meeting in Qunu, endorsed Makaziwe's comments. "I didn't see this with Margaret Thatcher or when George Bush was in hospital," she said. "The manner in which it's covered makes us incensed. Why don't people think, 'If it was my loved one, would I want all these details made public?'

"We appreciate all the love and support but the way it's done makes our blood boil. It's not been like this anywhere else. You guys want a pound of flesh. In the absence of details you speculate. We are going through a difficult time as a family and this doesn't make it easier."

Ndileka said she held media responsible but added: "I don't think the South African media would go to London and camp outside Buckingham Palace."

Mandela's eldest grandson, Mandla, also spoke out against the intensifying speculation. "I call upon those responsible to desist from spreading mischievous rumours about Madiba's state of health," he said, using Mandela's clan name. "Our government has been keeping all of us informed in this regard and there is no reason to doubt the accuracy of the information they provide to the public.

"At the end of the day my grandfather's fate like that of everyone else lies with God and our ancestors. However, many of us will continue to pray and hope for his recovery."

Mandela has spent 20 days in the hospital with a recurring lung infection – his fourth hospitalisation in six months. Many South Africans appear to be slowly coming to terms with the prospect of losing the father of the nation, who spent 27 years in prison resisting white minority rule.

How to cover Mandela's declining health has been a fraught topic in recent years. There was a lack of official information when he was hospitalised in January 2011. Later that year it emerged that two international news agencies had pointed hidden cameras at the former president's home, prompting headlines such as "Madiba spied on". A mutual distrust lingers between presidential spokesperson Mac Maharaj and some local and foreign journalists.

William Bird, director of Media Monitoring Africa, said: "Some media, and international media in particular, have revealed details that might be of interest to the public but are not in the public interest. This is understandable but not ethical. Against that, the kind of official information we've been getting is very limited. At least say, 'We saw him, he was awake or he wasn't.' They should have been trying to communicate a lot more."

He added: "The hype around it is pretty extraordinary. It's not comparison between Mandela and Thatcher, it's a comparison between Mandela and Princess Diana, and in that case there was a frenzy. At that time you saw similar rumours not about Diana's health but about how she died."

What was officially disclosed on Thursday yesterday gave a new flicker of hope. Zuma had cancelled an official trip abroad to visit Mandela at the Mediclinic heart hospital for the second time in less than 24 hours. He was informed by the medical team that Mandela had stabilised.

"I cancelled my visit to Mozambique today so that I could 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 respect for his privacy.

In her SABC interview, Makaziwe acknowledged that "anything is imminent. I can also state that God only knows when it is the time to go."

She continued: "We will live with hope until 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."

Officials did not deny claims that the statesman is on a life support machine. "Yes, he is using machines to breathe," Napilisi Mandela, a relative, 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 toys outside the hospital on Thursday and took them inside.

They gave thanks for the public's support. Members of a Salvation Army choir prayed and sang outside the hospital and the African National Congress (ANC) youth league paid tribute.

Crowds from South Africa and around Africa and the world gathered at the site as well as outside Mandela's former home in Soweto.

As many, including the government, continue to live on their nerves, there is little prospect of the media winding down. The US president Barack Obama arrives on Friday.