Holomisa, a close friend of the Mandela family who continues to advise them on many issues, said some of the statements made since the former statesman was admitted to hospital have angered and upset the family.
Mandela was rushed to hospital on Saturday June 15 and is being treated for a recurring lung infection at the Medi-Clinic Heart Hospital in Pretoria.
"Some of the family members were unhappy about the way his admission to hospital on Saturday morning was communicated because it tended to trigger panic buttons as many [of them] were not aware [of his condition]," said Holomisa.
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"Remember, it is a big family. I think [presidency spokesperson] Mac Maharaj tends to go too far, like when he said that Mandela was breathing on his own. Those things should be left to the medical doctors. The presidency should just tell us that he is in hospital and confirm where he has been admitted."
Holomisa also criticised ANC struggle veteran Andrew Mlangeni, who, during an interview, urged the family and South Africans to release Mandela spiritually and let him go.
"To the young members of the Mandela family, who do not know the cultural connotations of Mlangeni's statement, this was a complete shock. It was interpreted as if he wished him to die.
"As a friend of the family, it was felt he should have gone to the family and met the elders … and conveyed whatever he wished to have said. The fact that he went to the media infuriated the family," said Holomisa.
A month ago the ANC and its senior party leaders came under international and local criticism for visiting a clearly ailing Mandela.
The visit was then broadcast on SABC television, which showed images of a smiling President Jacob Zuma and ANC deputy president Cyril Ramaphosa with a frail Mandela, who showed no visible emotions.
This week Mandela's family reportedly issued instructions that nobody outside the family would be allowed to visit him in hospital.
However, ANC spokesperson Jackson Mthembu dismissed the reports, saying the family denied ever issuing an instruction that would essentially bar the ANC and government officials from visiting the former president.
Laloo Isu Chiba, a former Robben Island inmate and the man who helped write the manuscript of Mandela's autobiography Long Walk to Freedom, said he was saddened by the former president's medical condition.
"We hope the family will cope and are confident they will take things through with courage," said Chiba. "We feel their pain and we are with them in our prayers."