Mandela's grandson, Mandla, had revealed family secrets after a court ordered the remains of the three deceased children of the former president reburied in Mandela's home town.
Tutu, in a statement, said the legal quarrel was "almost like spitting in Madiba's face," The Guardian reported Friday.
"Your anguish, now, is the nation's anguish -- and the world's," said Tutu, who had worked for Mandela's release from prison. "We want to embrace you, to support you, to shine our love for Madiba through you. Please may we not besmirch his name."
Madiba is Nelson Mandela's clan name.
Mandela's oldest daughter, Makaziwe, had filed the suit against Mandla, who moved the bodies two years ago. Mandla said in a news conference his grandfather, who is hospitalized in critical condition, would be disappointed by the dispute.
The remains were re-interred Thursday in Qunu, where Nelson Mandela has said he wanted to be buried.