0832 GMT March 21, 2018
Zuma, who came to power in 2009, has been battered by a series of corruption scandals during his time in office, while the country has suffered record unemployment, slowing growth and stubborn racial inequality, AFP reported.
His removal of Finance Minister Pravin Gordhan last week unleashed a fresh bout of criticism, as Gordhan was seen by many ordinary South Africans as a bulwark against corruption.
Large crowds gathered in the capital Pretoria, the economic hub Johannesburg and coastal cities of Durban and Cape Town.
Several thousand people attended the Johannesburg protest organized by the opposition Democratic Alliance party, which hopes to make gains in 2019 elections under its leader Mmusi Maimane, 36.
The ANC party led the decades-long struggle against apartheid and carried Nelson Mandela to power in the 1994 elections that ended white-minority rule.
But the once all-powerful party has lost popularity in recent years and slipped to 55 percent of the vote in last year's local elections – its worst ever result.
Zuma this week appeared to have quelled a rebellion within the ANC despite senior party figures, including Deputy President Cyril Ramaphosa, speaking out against Gordhan's sacking.
On Friday, scores of camouflage-wearing members of MK, the former armed wing of the ANC, paraded at the party's headquarters in downtown Johannesburg in a show of loyalty to Zuma.
The cabinet overhaul – which was announced at midnight and including 10 ministerial changes – cleared out many of Zuma's critics.
It also led to a rapid credit ratings downgrade to junk status by Standard & Poor's.
South Africa's trade union federation Cosatu this week joined many anti-apartheid veterans, civil action groups and business leaders calling for Zuma to resign.
Zuma, 74, is due to step down as head of the ANC in December and as president ahead of the 2019 general election.
Zuma has been accused of being in the sway of the wealthy Gupta business family, allegedly granting them influence over government appointments, contracts and state-owned businesses.
Parliament will vote on a motion of no confidence in the president on April 18, though he has easily survived previous such votes against him.