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.