President Jacob Zuma, right, and the country's Deputy President, Cyril Ramaphosa, at an extended Cabinet meeting on January 31 to prepare for the president's state of the nation address.
There was also a call for an emergency National Executive Committee meeting, should Zuma dig his heels in and refuse to step down.
"The majority of parliament is going to say that Jacob Zuma will not be the president of South Africa because the biggest sentiment, even in the ANC, is saying that Jacob Zuma can not continue as president", EFF Deputy President Floyd Shivambu told eNCA television.
Julius Malema, an opposition leader and former ANC member, said on Twitter that Zuma had refused to stand down. The governing party's NWC last month mandated the top six officials to tell Zuma to resign, preferably before the upcoming state-of-the-nation address (Sona) on Thursday.
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An "urgent notice" sent to members of the NWC, a 26-member group that oversees the day-to-day operations of the party, scheduled the meeting on Sunday.
Zuma faces a growing chorus of calls for him to resign as president and is expected to meet the ANC's six most powerful officials this weekend, state broadcaster SABC said.
Zuma's job has been on the line since the December elective conference that saw Ramaphosa beating rival Dr Nkosazana Dlamini-Zuma and being named as the party's new leader.
Zuma is not due to leave office until the 2019 elections.
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On Friday Baleka Mbete, Speaker of the House, agreed to allow yet another vote of no confidence in Zuma, the ninth he will have faced, on February 22.
He has survived several no-confidence votes during his rule thanks to loyal voting by ANC lawmakers, who form a strong parliamentary majority.
Opposition parties have been calling on the ANC to remove the 75-year-old president, whose time in office has been marred by several allegations of corruption. The embattled Zuma told supporters at his 75th birthday bash in Soweto, Johannesburg previous year that he would resign should the ANC ask him to do so.
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