"If you're elected at one point, and people no longer want you, humble yourself, accept it," Zuma told thousands of supporters at a rally in northern Limpopo province to mark the 22nd anniversary of the election that brought anti-apartheid icon Nelson Mandela to power.
But Zuma also warned there could be no "shortcuts" to a shake-up at the top, saying any change of government had to come through "democratic institutions, so that we can have a peaceful state where the will of the majority prevails."
Today, hundreds of people demonstrated in Johannesburg, Cape Town and Durban to demand Zuma step aside.
Explaining the anger directed at Zuma, Ferrial Adam, one of the organisers of the Johannesburg protest, told AFP: "It's a combination of factors but people are quite angry and they don't feel empowered, they feel disregarded by the president."
"It's a movement with lots of diversity in terms of age, race and social background and it has the potential to grow," she added.
"We worked hard to build this country as millions of South Africans. It must not be destroyed by anarchists who have no interest in our wellbeing," Zuma said, referring to a threat by his former ally turned arch foe Julius Malema to remove the government through force.
In an interview last week with Al-Jazeera television, Malema, who heads the radical leftist Economic Freedom Fighters (EFF), warned: "We will run out of patience very soon and we will remove this government through a barrel of a gun".
Analysts say that if the party, which has been in power since 1994, loses control of one or more key cities, Zuma's leadership of the party -- and of the country -- could be in jeopardy.
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