Last year, S&P and Fitch downgraded the country's sovereign credit rating after Mr Zuma fired the finance minister over political infighting.
The group called themselves the concerned ANC members who love their organisation and would love to save it.
While the National Executive Committee (NEC), has the power to demand that Zuma step down, it does not wield the constitutional power to push him out of office.
If the motion were held and a majority of legislators voted against Zuma, the entire Cabinet would also have to resign, dashing Ramaphosa's hopes of a carefully managed transition.
"We all know and anticipate that they are dealing with the current issue that is facing our country", Faiez Jacobs, the party's provincial secretary, told eNCA television. He claimed that the group tried to persuade Zuma to go, but the president refused.
Ramaphosa, a 65-year-old lawyer and one of the richest black South Africans, has pledged to revive the flagging economy and clamp down on the corruption that Zuma's critics say have become synonymous with his rule.
Korea women's hockey team to make much-awaited Olympic debut
South Korea, which is using the Pyeongchang Games to break the ice with North Korea, seated its presidential couple alongside U.S. During the trip, Pence has kept up pressure on the north over its nuclear ambitions and human rights record.
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A delegation of MP's from the opposition parties has been led to Rashtrapati Bhavan by the Congress President Rahul Gandhi . The investigation should not be entrusted to either the CBI or the NIA, given their track record, the MPs said.
Tillerson in Egypt for start of Middle East tour
Tillerson is expected to meet various senior officials on the margins of both meetings before leaving the region February 16. This will be an opportunity to support the Iraqi people and help impart confidence that Iraq is now open for business.
The ANC leader said on Wednesday he and Zuma were holding direct talks over the transfer of power.
Maimane said if Ramaphosa could not remove Zuma‚ then either Parliament or South African voters must step in.
"We have no other choice but to continue fighting corruption" Ramaphosa said.
Most worrying for him is the expected reinstatement of 783 counts of corruption and fraud related to an arms deal.
Both men have been involved in talks around the South African president's voluntary resignation from office since last Tuesday, and public pressure on the ANC to finalise the matter increased as the dialogue dragged on. Other options for his removal include impeachment proceedings in parliament or a vote on an opposition-sponsored motion of no confidence that is scheduled for February 22.
The speaker of parliament, Baleka Mbete, has said she is considering their application. "We have further noted that certain individuals alleged to be ANC members, clad in ANC regalia, took part in an unmandated press briefing by the individuals in question earlier today".
Mr Ramaphosa has reportedly told ANC MPs that it is impossible to offer Mr Zuma immunity from prosecution.