Mandla Mandela _ the oldest male Mandela heir and a tribal chief _ told a news conference on Thursday that his grandfather "would be highly disappointed in what is unraveling."
Retired archbishop Desmond Tutu appealed to the family of Mandela, also known by his clan name Madiba, to overcome their differences.
"Please, please, please may we think not only of ourselves. It's almost like spitting in Madiba's face," Tutu said in a statement released by a foundation he leads. "Your anguish, now, is the nation's anguish _ and the world's. We want to embrace you, to support you, to shine our love for Madiba through you. Please may we not besmirch his name."
Mlawu Tyatyeka, an expert on the Xhosa culture of Mandela's family, said the court case over the graves was decided quickly because the family knows that Mandela will soon die.
"It's not a case of wishing him to die. It's a case of making sure that by the time he dies, his dying wish has been fulfilled," he said. "We have a belief that should you ignore a dying wish, all bad will befall you."
Meanwhile, Mandela's wife said the former president is sometimes uncomfortable but seldom in pain while being treated in a hospital.
Graca Machel spoke about her husband's condition at a fundraising drive for a children's hospital that will be named after Mandela.
"Whatever is the outcome of his stay in hospital, that will remain the second time where he offered his nation an opportunity to be united under the banner of our flag, under the banner of our constitution," she said.
Mandela was imprisoned for 27 years during white racist rule and was freed in 1990 before being elected president in all-race elections. He won the Nobel Peace Prize along with former President F.W. de Klerk.