JOHANNESBURG, South Africa - Nelson Mandela's grandson Mandla lashed out at family members Thursday, accusing them of publicly airing the family's dirty laundry in what has become an increasingly nasty battle over the former South African president's legacy.

The dispute has focused on family graves, but at its core is the question of who will succeed the iconic Mandela as head of the family. The question has become increasingly urgent as Mandela, 94, remains critically ill in a Pretoria hospital. Documents filed by family members in court last week said that Mandela has been on life support, and described his health as "perilous."

Mandela's wife Graca Machel told journalists in Johannesburg on Thursday that Mandela was sometimes "uncomfortable, but he has never been in pain." A statement from President Jacob Zuma's office described his condition as still "critical but stable."

More from GlobalPost: Meet Mandela's grandson, the gravedigger?

On Wednesday, police exhumed the bodies of Mandela's three deceased children from the homestead of eldest grandson Mandla, 38, following a court action led by the former president's daughter Makaziwe, his oldest surviving child.

Police this week confirmed that a criminal case of "tampering with graves" has been opened against Mandla Mandela following a complaint by family members.

Makaziwe and other family members say that Mandla moved the remains from Qunu village — to his own village of Mvezo — in 2011 without seeking permission or informing the rest of the family. The bodies were reburied Thursday in Qunu, where Mandela lived as a boy, and where in recent years he has spent much of his time.

Mandla, the traditional chief of Mvezo village, where his grandfather was born, held a press conference Thursday to respond to the court case and criticism from family members, who have told media that Mandla is an "illegitimate child" and “a power-hungry, self-obsessed man."

“I want to emphasize I don’t want to hang our dirty linen out in public," Mandla said at the briefing, before accusing his brother Ndaba of being born out of wedlock and announcing that another brother, Mbuso, had impregnated Mandla's wife.

Watch Mandla Mandela's full address to the media on Thursday:

Here's a taste of the public's at times horrified reaction:

[View the story "Mandela's grandson lashes out at family" on Storify]

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