"That we are Madiba's compatriots and that we lived in Madiba's time is a reason for great celebration," Zuma told tens of thousands of South Africans gathered at the World Cup stadium in Soweto used for the service.
"Everyone has had a Madiba moment. This world icon has touched their lives," he added, using the clan name by which many South Africans fondly refer to Mandela.
Before he spoke, Zuma had been repeatedly booed by sections of the crowd as his image flashed up on the big screens inside the stadium.
Most recently he was accused of spending USD 20 million of taxpayers' money to refurbish his private home.
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"In his honour, we commit ourselves to continue building a nation based on democratic values, of human dignity and democracy," he said.
"We'll continue building a nation free of poverty, hunger, homelessness.