In a ruling issued last week, a court said Mbeki’s government had interfered in the decision to prosecute Zuma.
All corruption charges against Zuma were also dismissed, paving the way for him to become South Africa’s president after next year’s election.
Zuma supporters have called for Mbeki to be thrown out of both the party and his office.
Half the cabinet is reportedly threatening to walk out if Mbeki is forced to leave.
Mbeki’s cabinet denies all claims of interference.
He issued a statement on Friday saying: “It impoverishes our society that some resort to the tactic of advancing allegations with no fact to support these.
“The question will have to be answered now – what kind of society are we building, informed by what value system and with what long-term effect to the political and overall moral health of the nation?”
Mbeki took over as president from Nelson Mandela in 1999, bringing sustained economic growth to the country.