He added that postponing the ruling ANC party's emergency talks "will enable President Zuma and myself to conclude our discussions and report back to our organisation and the country in the coming days".
At 0645 GMT, the rand traded at 12.0450 per dollar, not far off its NY close of 12.0650 on Wednesday. The initial domestic catalyst for rand strength was the election of new African National Congress (ANC) president, Cyril Ramaphosa.
"Local focus remains on the presidency".
"This is a challenging time for our country", Ramaphosa said in a statement.
In fixed income, the yield for the benchmark government bond due in 2026 was up 3.5 basis points to 8.435 percent.
While journalists set up camp under a tree opposite the entrance to the National Assembly on Wednesday morning, Speaker Baleka Mbete was inside the building with party chief whips for a special chief whips' forum meeting.
On Tuesday, South Africa's parliament took the extraordinary step of postponing Thursday's state of the nation address.
Leaders of various political parties held a crisis meeting in parliament Tuesday afternoon.
Both Mr Zuma and the Guptas deny any wrongdoing.
"The NWC (National Working Committee) has discussed the issue surrounding the future of President Jacob Zuma", Jessie Duarte told reporters.
He gave details of their meeting with Zuma and detailed how the president had asked them what the ANC meant by a "transition period". It also said Zuma would officiate at an awards ceremony in the city on Saturday.
"The fact that they cancelled Wednesday's ANC meeting probably means there is an agreement for him to go".
The 75-year-old has been South Africa's most controversial president since the end of white-minority rule in 1994, overseeing a tumultuous nine years marked by economic decline and numerous allegations of corruption.
Many graft allegations against him have centred on the wealthy Gupta family, who are accused of unfairly obtaining lucrative government contracts and even being able to choose ministerial appointments.
He said he needed to iron out some "pertinent matters" with Mr Zuma before the discredited president would step aside, however.