The document, known as a "certificate of urgency," was filed on June 26. It stated that the 94-year-old Mandela "has taken a turn for the worst and that the Mandela family have been advised by the medical practitioners that his life support machine should be switched off."
"Rather than prolonging his suffering, the Mandela family is exploring this option as a very real probability," it added.
The following day, however, South African President Jacob Zuma announced that Mandela's condition had improved from critical to critical but stable.
Mandela remained critical but stable Thursday, Zuma's office reported after he visited Mandela. It denied reports that Mandela was in a "vegetative state."
Considered the founding father of South Africa's modern democracy, Mandela has been hospitalized in Pretoria since June 8 for a recurring lung infection -- a legacy of his years of imprisonment under South Africa's now-defunct apartheid regime.
Another document filed by his family in a burial dispute described his health as "perilous" and stated that fears that his death is drawing near are justified.
That affidavit was lodged in court this week as 16 members of Mandela's family battled his grandson, Nkosi Zwelivelile Mandela, also known as Mandla, over where three of the anti-apartheid icon's deceased children should be buried.
Mandla Mandela lost his case Wednesday, which meant the return of the remains of the three relatives to the family graveyard in Qunu, Nelson Mandela's boyhood home, could go ahead.
They were reburied Thursday in the family compound.
The remains were removed from the Qunu village cemetery two years ago by Mandla Mandela and then taken to the village of Mvezo. The former South African president was born in Mvezo, but spent his childhood in Qunu.
The family affidavit lodged at the Mthatha High Court gives new insight into the seriousness of his condition.
"The anticipation of his impending death is based on real and substantial grounds," it reads.
"The applicants are desirous of burying their father and committing him to earth in which his descendants lie."
The family members said it is "incontestable" that the reburial of his three deceased children is what he wants.
"The applicants do not want a situation to be created in which Nelson Mandela's remains are committed to lie in a burial site, entirely alone and forlorn and absent from the remains of his children," the affidavit said.
The remains buried in Mvezo were found and taken to a mortuary Wednesday, Eastern Cape police said, according to the South African Press Association.
Forensic testing was done before the reburial in Qunu to confirm the identities of the bodies, the news agency said.
The three are Nelson Mandela's first daughter, Makaziwe Mandela, who died as a baby in 1948; his eldest son, Madiba Thembekile, who died in a car crash in 1969; and Makgatho Mandela, father to Mandla, who died in 2005, the news agency said.
Mandla Mandela issued a statement Wednesday saying he would abide by the court decision but continue "to fight for his right to put on record his side of the story."
On Thursday, he said his grandfather's health is the chief issue on his mind, the South African Press Association reported.
"My grandfather continues to be stable while in a critical space," he said.
"I want to focus on what matters most, being with my grandfather, ensuring I can be with him at this moment that he needs us most."
CNN's Robyn Curnow reported in Pretoria, Laura Smith-Spark wrote in London and Matt Smith wrote from Atlanta. CNN's Kim Norgaard, Tony Wende and Claudia Dominguez contributed to this report.