Mbeki has faced calls to quit before next year’s election from some quarters after the judge who threw out corruption charges against Zuma last week, Chris Nicholson, said there had been political interference in the case.
"President Mbeki must be given the opportunity to reply to this grave allegation. Unless he can convincingly rebut the judge’s opinion, this would constitute grounds for his removal from office," opposition Democratic Alliance (DA) leader Helen Zille said in a statement.
In his ruling Nicholson said there was a "titanic political struggle" between Mbeki and Zuma ahead of the African National Congress leadership election last December, in which Mbeki was defeated by the man he sacked as deputy president in 2005.
As leader of the ruling party, Zuma is almost certain to succeed Mbeki when he has to step down next year after serving two terms.
The ANC’s National Working Committee has been meeting to discuss a course of action after the allegations against Mbeki.
The militant youth league of the party said on Tuesday it would lobby the ruling party’s National Executive Committee to adopt a resolution to remove Mbeki. The committee is due to meet over the weekend.
The battle between Zuma and Mbeki for ANC leadership caused bitter infighting. The ANC, which prided itself on its iron discipline in the fight against apartheid, has ruled South Africa since apartheid ended in 1994.
Zuma has said there was no need for Mbeki to make an early exit and called for party unity ahead of the April elections.