Mandela, who in 1994 became South Africa's first black leader after the defeat of apartheid, was hospitalised early on Saturday when his frail health worsened.
It is his fourth hospital stay since December, when he spent three weeks in the care of medics, and the government said his condition was "serious".
Concern has increased among the millions of South Africans who revere Mandela for his decades of struggle against white-minority rule and for steering the continent's biggest economy to all-race elections.
Presidency spokesman Mac Maharaj said Mandela was breathing on his own in the Pretoria hospital, calling that a "positive sign".
Hundreds gathered to pray for Mandela at Sunday Mass at the Regina Mundi Catholic church in the Johannesburg township of Soweto.
"We wish him speedy recovery, he must get well," Soweto local Mlugisi Sekhosana said. "We know what he did for us in South Africa. All the nation, black and white, we wish him well."
A national newspaper took a sombre tone, with the headline "It's time to let him go", quoting a Mandela's longtime friend Andrew Mlangeni.
Mandela's most recent appearance in public was at the final of football's World Cup in Johannesburg in 2010.