"The public is urged to gather in halls, churches, mosques, temples, synagogues and in their homes for prayer services and meditation, reflecting on the life of Madiba and his contribution to our country and the world," President Jacob Zuma said in the statement.
Mandela, 95, died Thursday after a lengthy battle with a recurring lung infection. He was imprisoned for 28 years for plotting to overthrow South Africa's apartheid government, and was elected president in 1994.
Zuma attended a service at the Bryanston Methodist Church Sunday to celebrate Mandela's life.
"We should not forget the values that Madiba stood for and sacrificed his life for," he said.
Those in poor areas of South Africa gathered in fields to sing and pray for Mandela. Many migrants expressed concern that his death would lead to further troubles for them, the New York Times said.
"Nelson Mandela was a leader chosen by God, and now God has called him home," Virginia Sibanda, who lives in Diepsloot, a squatter camp, was quoted as saying. "He was a leader not just for South Africa but for all Africans, and the world."