Protesters are now marching in Johannesburg, Pretoria, Cape Town and other big metropolitan areas to push for the resignation of scandal-hit Mr Zuma.
Some protesters carried signs reading "Fire Zuma" while others said they felt the ruling class were more concerned about enriching themselves than dealing with high unemployment, a slowing economy and stubborn racial inequality.
Police said the number of anti-Zuma protesters outnumbered that of pro-Zuma marchers, who are staunch supporters of the ruling African National Congress (ANC). "There has been no such discussion", ANC spokesperson Khusela Sangoni said, when asked if the protests had led to any discussions in the party about Zuma.
Online Chat: DJ Kachman, the Veterans Affairs Department's director of mobile and security technology transformation lead, on April 10, at 1 p.m.
"South Africans will come together to protest our country being ruled by a clique that is determined to steal from the people and side-step accountability", Maimane said in a statement.
Fitch on Friday followed S&P Global Ratings and downgraded South Africa to "junk", citing Gordhan's dismissal as one reason. Past year the nation's graft ombudsman implied that Zuma allowed the Guptas to influence cabinet appointments and the issuing of state contracts.
Mr Zuma has said there was nothing improper in the way he chose ministers.
The ruling ANC said its members won't vote against the president, whose decision to change the cabinet was criticized by three senior members of the party, including Deputy President Cyril Ramaphosa. A year ago the party suffered key losses in municipal elections, and Mr. Zuma was forced, by a Constitutional Court ruling, to reimburse public monies in a dispute over millions of dollars he allegedly spent on his private home.
ANC secretary-general Gwede Mantashe told reporters that although the party had "reflected" on the resignation demands, "we won't recall President Jacob Zuma because opposition parties say so".
Outside Cape Town, retired archbishop Desmond Tutu, who is in frail health, made an appearance to support the protests.
Police fired rubber bullets and tear gas at some African National Congress protesters in Johannesburg, injuring a man and a woman, a Reuters witness said.
Members of the influential ANC Youth League gathered in downtown Durban, singing "Awuleth'umshini wami", a song popularized by Zuma, which means "bring me my gun" and held placards supporting the president.
Worldwide ratings agencies have downgraded South Africa and this will lead to high interest rates levied on home, vehicle and student loans, to high food prices and to a bigger fiscal debt.
A second ratings agency has downgraded South Africa to junk status.
Fitch claimed that the move reflects its views that recent political events, such as the cabinet reshuffle, will weaken standards of governance and as well as public finances.