While the political leadership has changed, the government's overall policy orientation remains the same as derived from the governing party, the African National Congress, said Zuma.
According to COSATU secretary-general Bheki Ntshalintshali, the unions no longer believe in Zuma's leadership capacity. The party later said the notes were sent in error and did not reflect the party's position.
He said details about the meeting would be revealed today. Nobody has a right to take that away from us as citizens. Zuma has denied any inappropriate influence on his selections, and the Guptas deny wrongdoing. "We will not allow that".
The ANC thanked Jonas on Twitter "for his selfless service to the movement as its public representative".
COSATU was instrumental in Zuma's rise to power in 2009, writes South Africa's Mail & Guardian newspaper. That is why he was sacked.
The events that unfolded after the reshuffle had "created anxiety and undue confusion as a result of the discordant views, in particular of the National Officials of the ANC", Mantashe said, referring to the criticism directed at Zuma.
Cosatu's call for him to step down is a crushing blow to the beleaguered head of state.
Zuma's cabinet reshuffle, in which he also sacked some critics, has brought an official request by the opposition Democratic Alliance for a vote of no confidence in parliament and plans for protest marches.
Zuma has been under fire for several days - including from within his own camp - after dismissing Gordhan, a decision that caused the rand currency to plummet. The parties said they are "united in their call for Zuma to go and our belief in the supremacy of the Constitution".
Zuma's fresh "transformation" pledge has been criticised by opponents who say it is a populist attempt to win votes and vague rhetoric similar to many promises made since the end of apartheid in 1994.
Also present were mayor Athol Trollip and religious leaders.
However, supporters of Zuma, like the ANC Youth and Women's Leagues, are planning pushback campaigns, including celebrations to mark Zuma's birthday next Wednesday.
"Let us act together in unity!"
"The fact is that the minister is just not up to the job", the DA said in a statement.
The Gigaba entourage includes political adviser Thamsanqa Msomi, who serves on the Denel board and has been reported to have Gupta links, and legal adviser Kholeka Gcaleka.
Selfe said ratings agency Standard & Poor's decision to downgrade South Africa's credit rating to junk status was due to Gordhan's removal.
"We acknowledge yesterday's announcement was a setback... but now is not a time for despondency", he told a media conference.
He also disclosed that he had spoken to Moody's and Fitch on Friday.