"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."
The "Certificate of Urgency" document was filed by a lawyer representing Mandela family members who had successfully sought a court order to return the disputed children's remains to the revered South African leader's childhood home, after a grandson had them moved to his own village.
The document was presented to South Africa's Eastern Cape High Court as President Jacob Zuma reported that Mandela's health had faltered and cancelled a trip to Mozambique.
The next day Zuma reported that Mandela's condition had "improved during the course of the night".
"He is much better today than he was when I saw him last night. The medical team continues to do a sterling job," Zuma said in a statement dated June 27.
Since then the government has said Mandela's condition remains "critical but stable", but has provided few details, citing patient confidentiality.
Lawyers for Mandela's relatives, family members themselves and government officials were not immediately available for comment.