On Thursday, a Home Affairs department spokesperson told SBS News it was now "monitoring the situation of minority groups in South Africa" and considering "potential resettlement under the offshore humanitarian program".
The spokesperson did not specify which minority groups, but white people only make up about 10 per cent of the population in South Africa.
The offshore humanitarian program makes up the majority of Australia's refugee intake and saw nearly 12,000 people settled last year.
"If you look at the footage, you hear the stories and you read the accounts, it's a horrific circumstance that they face," Mr Dutton told News Corp on Wednesday.
The senior Turnbull government minister, who still oversees immigration in his expanded Home Affairs portfolio, credited stories in News Corp publications for bringing the matter to his attention.
"I've asked my department to look at options and ways in which we can provide some assistance because I do think on the information I've seen people do need help, and they need help from a civilised country like ours."
Mr Dutton told 2GB radio on Thursday white farmers in South Africa were also facing a new plan from the government to reclaim farmland without compensation.
"I think in this circumstance we do need to look at the persecution that's taking place," he said.
"I do think on the information that I've seen, people do need help, and they need help from a civilised country like ours," Mr Dutton said.
He suggested an announcement could be made soon.
South Africa insists 'threat does not exist'
South Africa’s foreign ministry has dismissed Mr Dutton's comments and expressed its "regret" over the lack of diplomatic communication.
"That threat does not exist," the South African foreign ministry in Pretoria told Reuters.
"There is no reason for any government in the world to suspect that a section of South Africans is under danger from their own democratically elected government.
"We regret that the Australian government chose not to use the available diplomatic channels available for them to raise concerns or to seek clarification."
South Africa's ruling ANC party is planning new laws that will allow the government to redistribute farmland without paying compensation, in an escalated push to give black South Africans more access to the land.
White farmers are a racial minority in South Africa but own a disproportionate amount of farmland, as a legacy of the country's apartheid era.
The government has been buying back land from white farmers for years but has been frustrated by slow progress in increasing the percentage of black ownership.
AfriForum, a rights group representing primarily the white Afrikaner minority, praised Mr Dutton's comments but said it was not in favour of mass emigration, Reuters reported.
"Our future is in Africa, not elsewhere," chief executive Kallie Kriel said.
- with AAP