The ANC had earlier rejected a debate on the motion, saying it was "frivolous".
A statement released on Wednesday by the spokesperson of the ANC chief whip, Mathole Motshekga, said this "reaffirms the ANC's commitment to robust, open and free multiparty debates".
This heads off a debate, scheduled on the parliamentary programme for Wednesday, on whether the motion of no confidence should be debated. It's unclear whether it will have an impact on a high court case concerning the matter.
Opposition parties have pushed for the debate to be heard before Parliament closes its formal sittings next week and the Democratic Alliance last week filed papers in the Western Cape High Court to compel speaker of the House, Max Sisulu to "take whatever steps are necessary" to ensure that the motion is debated by Thursday, November 22.
Earlier this week the high court judge, Dennis Davis, lashed out at the politicians for rushing to courts to decide on the matter, saying it was ridiculous to put so much pressure on judges on something so important.
"Can the courts start saying to Parliament, sorry you have to rearrange your schedule? The case has enormous implications.
"Courts are increasing getting drawn into difficult issues.
"How do I tell the speaker and the chief whip that as a Judge, I think your priorities were wrong?"
Davis reserved judgment on the matter until Thursday morning.
Motshekga's office said the position it took on Wednesday does not seeks to pre-empt or interfere with the court process, "but to correct the inaccurate view that the majority party is not keen on debating this motion".
According to the office and the parliamentary programme, MPs will be busy with committee meetings, oversight visits across the country and international study tours from November 26 to December 7.
Cancelling these commitments or summoning back all MPs for a special sitting would be a place a significant administrative, logistical and financial burden to the institution, it said.
All motions and business on the programme of Parliament lapses at the end of the last day of the sitting of the house but the ANC said it would commit to supporting the revival of the motion to ensure that it returns to the House next year.
Constitutional law expert Pierre De Vos however said the party's about face on the matter was an admission that its original decision was not constitutionally tenable and an indication that they thought they were going to lose the court case.
"I suspect they might probably have saved themselves from being ordered by the judge to hear the debate," he said.
De Vos said that he doubted the ANC would have changed its position if not for the threat of court action.
"In a way it's a good thing because the system worked. The threat of court action allowed the appropriate body [Parliament] to make the decision," he said.
Political analyst Ebrahim Fakir, meanwhile, warned that the dispute could diminish levels of cooperation between the ANC and opposition parties.
He said that while the DA had secured a strategic victory from the ANC by demanding a debate on the vote of no confidence, it would not be without consequences for society, he said.
The country still needs to deal with fundamental issues, like tackling inequality and developing a new social compact, he said, and this would need a great degree of compromise.
"In a political culture built on compromise and consensus building on important issues, this level of polarisation in the political [arena] can be ill-afforded," he said.