Retreating from an initial decision by the ANC's Parliamentary caucus to quash the motion, secretary-general Gwede Mantashe said the matter would be debated, but not immediately.
"The ANC cannot refuse to discuss a motion of no confidence, but we will not be frogmarched into doing so. It is not an urgent matter," he told journalists in Johannesburg.
The decision comes a day before an urgent interdict to debate the matter was to be heard in the Western Cape High Court.
The ruling party has labeled the motion of no confidence tabled against the president on Thursday as a "playful, silly publicity stunt" that "belongs to the rubbish bin".
Opposition parties, including the African Christian Democratic Party, Azanian People's Organisation, Congress of the People, the Democratic Alliance, the Freedom Front Plus, the Inkatha Freedom Party, the United Christian Democratic Party and the African People's Convention, tabled the motion in the National Assembly on Thursday last week.
The parties said the motion was motivated by the Marikana killings; the Nkandlagate scandal; the failure by the government to deliver textbooks and workbooks to school children in Limpopo and the Eastern Cape; the downgrading of South Africa's credit rating by two major ratings agencies; the mounting disrespect for our Constitution and judiciary; unemployment; and the "uncontrollable and rising tide" of corruption in the public service.
Shortly after DA parliamentary leader Lindiwe Mazibuko tabled the motion, the ANC tabled a counter-motion proposing that Parliament reaffirm its full confidence in Zuma's leadership.
In a statement released shortly afterwards, the ANC said it had reaffirmed its "resolve to quash any frivolous and narrow publicity-seeking gimmicks masquerading as motions in the National Assembly by some opposition parties".
Moloto Mothapo, spokesperson for the party's chief whip, said that the motion was not based on any fact or evidence, and therefore amounts to nothing but character assassination.
However, according to legal experts, the ANC soon realised its decision to oppose the motion was unconstitutional.
"The ANC can't decide what is debated upon. That's illegal. They can merely decide how to prioritise the matter as they have done now," constitutional law expert Pierre de Vos told the Mail & Guardian.
The motion of no confidence was largely interpreted as a move by opposition parties to sound out MPs who had become disenchanted with Zuma's leadership in the run up the ANC elective conference in Mangaung.
As such, opposition parties requested the vote to be held by secret ballot.
Mantashe gave no indication as to when the matter would be given the go ahead to be discussed in Parliament.
However, with the current session of Parliament due to close in early December, it is likely the matter will only be addressed in the new year.