After a marathon eight-hour meeting of the party’s top leadership, party leader Cyril Ramaphosa delivered the message to Mr Zuma in person, the SABC state broadcaster said.
Mr Ramaphosa’s motorcade returned an hour later to the venue of the ANC meeting debating Mr Zuma’s fate.
Mr Zuma has faced mounting calls from his party to end his scandal-plagued second term a year early since Mr Ramaphosa was voted in as party leader in December.
Motion of confidence against South African president Zuma falls
The NEC meeting in a Pretoria hotel had all the ingredients for a showdown between Mr Zuma’s supporters and those backing a swift transfer of power to Mr Ramaphosa.
On Sunday, the 65-year-old said the meeting was expected to “finalise” the situation.
The party executive has the authority to order Mr Zuma to step down as head of state, although there is some domestic media speculation he might refuse.
Calls for Zuma resignation in Pretoria
Since becoming president in 2009, Mr Zuma has been dogged by scandal.
Mr Ramaphosa has put the focus on rooting out corruption and revitalising economic growth.
Additional reporting by Reuters