"If Zuma's demands are met by the ANC, it would be a damning indictment on ANC president Cyril Ramaphosa who has chosen to negotiate a dignified exit for the man faced with 783 counts of corruption, fraud, money-laundering and racketeering, who was at the heart of the Nkandla scandal and who likely facilitated state capture", Selfe said.
ANC National Chairperson Gwede Mantashe opens proceedings at the Mandela centernary celebrations in Cape Town.
The Top Six backed Ramaphosa fully and resolved that there was no longer any point in continuing to "manage the transition" with Zuma, and that he should therefore go.
The national executive committee (NEC) would meet on Monday "to discuss and finalise this matter".
Zuma has clung to power after rejecting a request by his party's senior officials to resign a week ago.
Many of Zuma's former supporters want him to resign because of his links to scandals that have sapped support for the ANC and hurt the economy.
The Democratic Alliance, South Africa's largest opposition party, has said Zuma "must be prosecuted and, if found guilty, be locked up for his crimes".
"We know you want this matter to be finalised. The (ANC parliamentary) caucus is also prepared to facilitate Zuma's departure".
"No single SOE will work or operate in the interests of individuals or certain families".
Last year, S&P and Fitch downgraded the country's sovereign credit rating after Mr Zuma fired the finance minister over political infighting.
"We have no other choice but to continue fighting corruption" Ramaphosa said.
It was in that same vast square in front of City Hall on February 11, 1990, that Nelson Mandela spoke to a euphoric crowd hours after his release from prison.
He said 2018 will be the year of continuing Mandela's legacy of fighting corruption, and that those who are corrupt, and stealing from the poor, will be brought to justice.
"That is what Mandela would have wanted".
"We commend the people of the Western Cape for confronting this crisis".
Ramaphosa, who only just won a bitterly fought internal election to become president of the ANC, has the support of only just over half the members of its top decision-making body.
"We have arrived at a moment in the history of our country where we can relive that moment when Nelson Mandela was released".