"My grandfather, like myself, would be highly disappointed in what is unravelling," he told reporters in Mvezo on Thursday, referring to the family's feud over the burial place of Mandela's three children.
The remains are those of Mandela's eldest son Makgato Mandela, who died in 2005; Mandela's first daughter Makaziwe, who died as an infant in 1948; and Mandela's second son Madiba Thembekile, who died in a car accident in 1969.
Mandla Mandela allegedly moved the graves from Qunu to his home in Mvezo in 2011.
Mandela "would have asked every member of the family if there are any secondary thoughts on his recommendation. I am here because of his own grooming and recommendation," Mandla said.
Mandla Mandela spoke in detail on how his grandfather had taught him from a young age about taking over the village.
He said his grandfather's last will and testament remained a secret, and remained with people he appointed to administer it.
"I received an instruction [from] my aunt Makaziwe [Mandela] to remove remains [from Mvezo] and bury them in secret in Qunu where she is preparing a grave for my grandfather," he said.
"I didn't follow those instructions, because [it was] not coming from my grandfather, I took the remains and kept them here [in Mvezo] until I received information from my grandfather or instructions from his spouse Graça [Machel]."
Meanwhile, Mandla Mandela said he was disappointed by the court decision and was convinced it was erroneous.
The Eastern Cape High Court in Mthatha on Wednesday dismissed Mandla Mandela's application to halt the exhumations of Mandela's three children.
A group of Mandela family members approached the court to have the remains exhumed and moved back to the family graveyard in Qunu. They were removed on Wednesday.
The grandson of the former president said he wanted to talk about the real reasons why the matter emerged and why his family had turned against him.
"This is the very family who has taken their own grandfather to court for his money. I called this press conference so that I could address a few matters circulating in the media."
He was referring to the court case by Mandela's two daughters, Makaziwe Mandela and Zenani Dlamini, to have the directors of companies set up to manage royalties from the sale of Nelson Mandela's artworks removed from their posts.
They want 'to use me for popularity'
Also on Thursday, Mandla Mandela said that he seemingly angered people by distancing himself from the legal challenge involving the ailing statesman's estate.
He was referring to the legal challenge by Mandela's two daughters against the trustees of Mandela's will over investment companies.
"I still refuse to be associated with the court actions that are a clear squabble over my grandfather's money. This too shall come to [the] surface," he said.
"I am tired of people who want to use me for popularity and short-term gains."
Ndaba 'wants to throw insults'
Mandela on Thursday added that he is "highly disappointed" at his brother Ndaba for claims he made to the media.
"He claims in media reports I was born out of wedlock. I wish he would say that in the presence of my father," he said.
"I want to remind him that I do not hand out our dirty linen as a family in public. He knows very well that my father impregnated a married woman … he is a result of that act.
"He should be very careful when he wants to throw insults, particularly to my mother, who still sits by my side, nurtures [me], and ensures I can wake up every day to serve my community." – Sapa