PRETORIA, South Africa — Singing crowds gathered outside the hospital where Nelson Mandela, South Africa’s former president, lay in a critical state for a third consecutive day on Tuesday, as family members held an emergency meeting at his ancestral village.

Mr. Mandela’s eldest daughter, Makaziwe, at least two grandchildren and clan elders gathered at Mr. Mandela’s retirement house in Qunu, the remote southern village where he grew up, according to news media reports.