The party's powerful 107-member national executive committee (NEC) met at a hotel outside Pretoria, but gave no official update on Zuma's fate after several hours.
The committee could "recall" the head of state, essentially ordering him to step down, although he would be under no constitutional obligation to obey.
He would then likely be ousted via a parliamentary vote of no-confidence within days.
African National Congress chief Cyril Ramaphosa -- the de-facto president-in-waiting -- has been in negotiations with Zuma, who rejected a request from party leaders to step down more than a week ago.
The stalemate has plunged South Africa into political uncertainty over who is running the country, with a series of public events cancelled including last Thursday's State of the Nation address to parliament.
"We know you want this matter to be finalised," Ramaphosa, 65, said at a party rally in Cape Town on Sunday to rapturous cheering.
"We know you want closure... Because our people want this matter to be finalised, the NEC will be doing precisely that."
South African opposition parties on Monday called for early elections as the ANC's leadership battle ground on.
"We must proceed to the dissolution of parliament... subsequent to that, we move on to an early election," Democratic Alliance (DA) party leader Mmusi Maimane told reporters, speaking alongside several opposition parties.
The parliamentary speaker announced that an opposition request for a no-confidence vote against Zuma on Tuesday was still being considered on Monday evening.
Some members facing corrupt allegations while serving under Zuma are "not fighting for a principle or the ANC, it will be the basic instinct of self-preservation," he told eNCA television.
"They will strive for consensus, but if that fails, it will go to a vote," he warned.
"The pressure is so much, it has to be the final decision for the ANC leadership. If they fail to do so, they will have surrendered the initiative."
Zuma's presidency has been marred by corruption scandals, slow economic growth and record unemployment that have fuelled public anger.
He was due to stand down next year after serving the maximum two terms after coming to power in 2009.
Zuma's hold over the ANC was shaken in December when his chosen successor -- his former wife Nkosazana Dlamini-Zuma -- narrowly lost to Ramaphosa in a vote to be the new party leader.
A key sticking point in the negotiations is reportedly the potentially ruinous legal fees Zuma faces from prolonged court battles against multiple criminal cases.
He is also said to be seeking legal protection for his family and other associates who have been involved in controversial deals.
The ANC has insisted there will be no delay to the budget, which is due on February 21.
Sunday's rally was part of ANC celebrations marking 100 years since Nelson Mandela's birth -- as well as efforts by Ramaphosa to revive the party's tainted reputation ahead of next year's general election.
Zuma, 75, has not spoken publicly since being asked to resign by senior ANC officials on February 4.
In 2008, his supporters pushed out then-president Thabo Mbeki over allegations of abuse of power.
Under Zuma, the ANC won less than 54 percent of the vote in local elections in 2016 -- its worst electoral performance since coming to power with Mandela at the helm in 1994.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)