Called the Freedom Movement and backed by retired archbishop Desmond Tutu, it plans to hold a mass rally on April 27, the annual holiday marking South Africa's first post-apartheid election in 1994.
Zuma's sacking of respected finance minister Pravin Gordhan last month fanned years of public anger over government corruption scandals, record unemployment and slowing economic growth.
"Never before has there been a more urgent need to build unity of purpose to stop South Africa's current trajectory," said the movement at its launch in Soweto, a hotbed of the struggle against apartheid.
"State capture" is a term that refer to the alleged corruption among Zuma and his associates.
Tens of thousands of South Africans have in recent weeks staged demonstrations demanding Zuma's resignation.
The main opposition Democratic Alliance party and several small opposition parties backed the alliance as well as some trade unions and the National Religious Council.
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