The South African spokesman said their foreign office had also received an effective retraction from the prime minister, via Australia's ambassador.
"We also had a meeting with the high commissioner [ambassador] who conveyed a message from the prime minister, who said the same thing, to indicate that this is not the view of their government," Mr Mabaya said.
Hours later, a spokesman for Australia's Home Affairs Minister told The Australian that South Africa’s comments did not "accurately reflect" the position of Mr Turnbull or Ms Bishop.
"There was no rebuttal of the words of Minister Dutton," the spokesman said.
A spokeswoman for Ms Bishop told SBS News: "The Prime Minister and the Ministers for Foreign Affairs and Home Affairs have been clear and consistent in reiterating that Australia’s current humanitarian visa program is non-discriminatory, with each application assessed on its merits. The program can accommodate those fearing persecution."
Opposition leader Bill Shorten said he "didn't know" what was motivating Mr Dutton's comments, but then said they were an appeal to conservatives within the Coalition to improve his chances of securing the leadership one day.
"If Mr Dutton wants to enter a beauty parade to win the right wing of the Liberal Party for votes in the future to undermine Mr Turnbull, that's a matter which is up to them," the Labor leader told reporters in Melbourne.
Mr Turnbull said South Africans who felt persecuted at home could apply for a humanitarian visa to come to Australia like anyone else.
"It is non-discriminatory and it is a very generous program, people in South African who feel that they have been persecuted are certainly able to apply, there is no question about that," Mr Turnbull told ABC Radio.
Mr Dutton's original comments did call for "special" consideration under the existing humanitarian program, and the Home Affairs deparment confirmed it was considering "potential resettlement" offers for persecuted minorities.
Foreign minister Julie Bishop said there were no plans to change the "non-discriminatory" nature of the refugee visa, but said she was "working with the home affairs minister to ascertain if any changes are needed".
Mr Dutton's offer to help settle persecuted farmers in a "civilised country" like Australia drew an angry response from South Africa, kicking off a diplomatic row.
Mr Dutton's comments have found support among conservatives in the parliament. Backbench Liberal Andrew Laming and independent Fraser Anning, once of One Nation, spoke at a march in support of white farmers in Brisbane recently.
Senator Anning told SBS News he would support any move to extend special consideration, describing the violence as an attempted "genocide" of white South Africans.
- with AAP