South Africa’s governing party, the ANC, has postponed a top-level meeting that was expected to decide on President Jacob Zuma’s future.
Instead the ANC released a statement saying it had held “fruitful and constructive discussions” with him.
Mr Zuma is under growing pressure from members of own party to resign amid corruption allegations.
Earlier on Tuesday, parliament took the extraordinary step of postponing Thursday’s state of the nation address.
South Africa’s Times Live website quoted unnamed sources as saying Mr Zuma was prepared to quit, if the right terms can be negotiated.
The formal National Executive Committee (NEC) meeting has been set for 17 and 18 February, the ANC’s party leader, Cyril Ramaphosa, said in a statement.
The high-level group has the power to remove the president from office without his agreement.
Opposition parties are demanding that a vote of no-confidence be held to remove him.
Mr Zuma, 75, was replaced as party leader by Mr Ramaphosa, his 65-year-old deputy, in December. Mr Ramaphosa is set to succeed him as president.
Earlier on Tuesday, the Nelson Mandela Foundation urged Mr Zuma to step down.
South Africa had seen “systematic looting” under Mr Zuma’s rule, and he “must go sooner rather than later”, the foundation said in a statement.
The ANC had said it would make a final decision on Mr Zuma’s future at Wednesday’s NEC meeting.
If the ANC had decided to withdraw all their support, President Zuma would not have a majority in parliament, making it hard for him to resist.
Emergency party talks were held in Johannesburg on Sunday. Those attending were said to be largely, but not entirely, in agreement.
Mr Zuma also met top ANC leaders on Sunday. They are said to have failed to convince him to stand aside then.
Other unconfirmed reports from Sunday’s meeting say Mr Zuma asked for protection from prosecution for himself and his family.
The state of the union address – always made by the sitting president – is the main political event of the year in South Africa.
Parliament cancelled it out of concern over “calls for disruption”, according to Speaker of the National Assembly Baleka Mbete.
Mr Zuma’s office said in a statement that “the president has requested the postponement due to certain developments”.