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.
Local media said the meeting continued into the night after a presidential spokesman denied reports that a resignation deal had been agreed.
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."
"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.
Political analyst Somadoda Fikeni said the ANC committee appeared split.
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.
"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.
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.
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.
Ramaphosa is a former trade unionist who led talks to end apartheid rule in the early 1990s and then became a multi- millionaire businessman before returning to politics.
Disclaimer: No Business Standard Journalist was involved in creation of this content
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
