South Africa's largest trade union and ruling African National Congress (ANC) party ally Cosatu, will meet President Jacob Zuma "as soon as possible" at his request.
Sizwe Pamla, the union's spokesman, said the meeting will discuss the cabinet reshuffle that has cost the country one investment-grade rating and deepened a rift within the ANC.
Cosatu called on Zuma to quit on Tuesday, in the wake of the cabinet reshuffle last Thursday where he fired 15 ministers and deputy ministers including finance minister Pravin Gordhan.
The ANC leadership on Wednesday said it was backing Zuma, Secretary General Gwede Mantashe said.
Mantashe said the ANC had accepted the "irretrievable breakdown of the relationship" between Zuma and the former finance minister as the reason Gordhan was sacked.
Gordhan's departure and those of his cabinet colleagues outraged Zuma's opponents and even some of his allies, undermining his authority as president and threatening to split the ruling ANC, which has governed South Africa since the end of apartheid in 1994.
The rand, which fell as much as 1.9 percent at the start of trading on Tuesday, turned 1 percent firmer through the day as calls for Zuma to quit came in from unions, religious leaders, civil society and the opposition, although one analyst said he retained strong support within the party.
The ANC said late on Tuesday that it will address media on decisions made after two days of meetings.
Cosatu criticised Zuma's move saying it no longer believed in his ability to lead, and that it wanted to restructure its alliance with the party.
Zuma himself, in his first public comments since he fired Gordhan, said that fiscal policies would be unchanged and that people should remain calm.
Rating agency S&P Global Ratings cited Gordhan's dismissal as one reason for its downgrade of South Africa to "junk" in an unscheduled review on Monday.
In a bid to reassure markets, Zuma said he expected the addition of "many young ministers" to "add renewed energy into Cabinet and the executive."
"With regards to the finance portfolio, we reiterate that while the political leadership has changed, government's overall policy orientation remains the same."
He called for a truce within the government as well, saying public disagreements "demoralise our people and create confusion."
Cosatu is the second biggest ANC ally to call on Zuma to quit after South Africa's Communist Party urged him to step down last Friday.
Malusi Gigaba, the country's new finance minister, told a news briefing he would address the issues raised by ratings agency Standard & Poor's.
The junk status rating by S&P will push up borrowing costs and put an even greater focus on growing the economy.
But deputy central bank governor Daniel Mminele said the downgrade was a serious setback and the bank would act if political events caused the favourable interest rate outlook to reverse, suggesting it may have to contemplate rate hikes.
Half of the ANC's top six group of officials including Deputy President Cyril Ramaphosa and Secretary General Gwede Mantashe have publicly criticised Gordhan's sacking.
But Zuma, also one of the top six, has the support of two other members and influential groups within the ANC, sources said.
The main opposition party - which has called for a no-confidence motion against Zuma - wants parliament to return from recess to debate the "crisis" triggered by the reshuffle.
Previous no-confidence motions in parliament against Zuma have failed as the ANC has a commanding majority there.