The ANC, which ousted Mbeki over the weekend, has recommended its deputy president, Kgalema Motlanthe, for that post.
Jessie Duarte, an ANC spokeswoman, told 702 Talk Radio in Johannesburg, the commercial capital, on Tuesday that the party wants Motlanthe as acting president so that Zuma could be elected next year with "a fresh mandate.''
Mbeki's departure was forced in part by accusations that he interfered in the prosecution of his rival, Jacob Zuma.
The African National Congress party (ANC) is divided between supporters of Mbeki and his rival, Jacob Zuma, the ANC leader.
Zuma, the man expected to become South Africa's next president when elections are held in 2009, is not eligible to replace Mbeki at this stage because he is not a member of parliament.
Zuma's supporters say they wanted the cabinet to stay in place to ensure a smooth transition.
Mbeki to appeal
Jane Dutton, Al Jazeera's correspondent reporting from Cape Town, said: "There haven't been any mass resignations, certainly not as yet, most of the resignations are expected to happen after the new president is sworn in on Thursday.
"Phumzile Mlambo-Ngcuka's resignation now paves the way for Motlanthe to take over the position of president tomorrow here in parliament.
"Thabo Mbkei says he wants to fight back ... to clear his name, and he is appealing to the highest court in the land, the constitutional court. Because he feels he was unfairly implicated in the Jacob Zuma case, so he is asking for a retrial."
Mbeki had faced criticism over allegations that he pushed for corruption charges to be brought against Zuma.
A court ruling, handed down on September 12, threw out charges of corruption against Zuma, saying the prosecuting team violated some of his procedural rights.
Bulelani Ngcuka, the former prosecutor, said in 2003 that there was a case against
Zuma, but did not press charges because, in political terms, he said the case
The national assembly formally adopted a motion by 299 to 10 votes on Tuesday,
accepting Mbeki's resignation and thanking him for his service to the nation for the past 14 years as deputy and then national president.
The main opposition Democratic Alliance voted in favour of the motion but
said it was troubled by the ANC's behaviour.
Sandra Botha, the alliance's leader, said: "The ANC's decision to force the resignation of President Thabo Mbeki was motivated purely by revenge and the desire to settle political scores.
"It has nothing to do with the interests of the people of South Africa."