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The government has released few details about Mr. Mandela’s condition, citing patient confidentiality and appealing for Mr. Mandela’s privacy and dignity to be respected. But rumors and unconfirmed reports about his health have persisted on social media and other forums, fueled in part by the family feud.

In a court case stemming from the dispute over burial sites, some members of Mr. Mandela’s extended family recently said in court documents that he was being kept alive by a breathing machine and faces “impending death.” That account was disputed by Mr. Zuma’s office, which denied that Mr. Mandela was “vegetative” but acknowledged his condition was grave.

Mr. Mandela has been particularly vulnerable to respiratory problems since contracting tuberculosis during his 27-year imprisonment. The bulk of that period was spent on Robben Island, a prison off the coast of Cape Town, where Mr. Mandela and other apartheid-era prisoners spent part of the time toiling in a limestone quarry.

There has been an outpouring of concern in South Africa and around the world for the transformative figure who led the tense shift from apartheid’s white minority rule to democracy two decades ago. Mr. Zuma urged South Africans to accept that Mr. Mandela had grown old and frail, saying all they could do was pray for him.

Mr. Mandela, a Nobel Peace Prize laureate, is feted around the world as a towering figure of reconciliation. Despite being jailed for his prominent role in opposing white racist rule, he was seemingly free of rancor on his release in 1990, becoming the unifying leader who led South Africa through a delicate transition to all-race elections that propelled him to the presidency four years later.

The United Nations has recognized Mr. Mandela’s birthday, July 18, as an international day to honor themes of activism, democracy and responsibility embodied by the former leader.