Mr Dutton's office told SBS News the minister had no comment on the demand, while foreign minister Julie Bishop said the South African government should focus on its problem with violent crime.
"The message that we urge on the South African government is that they seek to ensure the security of all their citizens and we certainly urge the South African government to ensure that any changes to land ownership, for example, are not disruptive to the economy nor lead to violence," she told ABC Radio.
The building diplomatic stoush began when Mr Dutton revealed he had asked his department to "look at options" to help the country’s “white farmers” on Wednesday, citing recent reports of violent attacks.
“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 said.
On Thursday, the department confirmed to SBS News it was now "monitoring the situation of minority groups in South Africa" and considering "potential resettlement under the offshore humanitarian program".
Mr Dutton’s comments come as the South African government moves ahead with a plan to take over farmland “without compensation" to redress land confiscations of the colonial and apartheid era.
According to police, 74 farmers were murdered between 2016 and 2017 in South Africa, which has one of the world's highest crime rates.
The African Farmers Association of South Africa said it was "offensive for the minister to polarise agriculture".
"He is bringing a racial dimension into a socio-economic issue," said spokesman Neo Masithela. "Transformation has been extremely slow, it is a very emotional issue."
Land is a hugely divisive topic in South Africa, where 72 percent of individually-owned farms are in white hands 24 years after the end of white-minority apartheid rule.
By contrast just four percent of such land is owned by black people, according to an audit cited by President Cyril Ramaphosa.
Dutton suggested that white South African farmers could apply for humanitarian visas typically sought by Iranian, Iraqi and Somali asylum seekers.
"If you look at the footage and read the stories, you hear the accounts, it's a horrific circumstance they face," Dutton told The Daily Telegraph.
Another Australian cabinet minister, Steve Ciobo, agreed the farmers' situation was "cause for concern".
"Let's be frank, if we see in this case, people who are being thrown off their land, being persecuted, I've read of people being shot, rapes, all sorts of different things, then I do believe that there's a role to be played," he told the ABC.
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.
The South African government has not yet spelt out exactly how land would be redistributed.
"We must, given the history we have had, work with urgency to significantly and sustainably escalate the pace of land reform," South African president Cyril Ramaphosa told parliament on Wednesday.
Dutton has doubled down on his plan to bring white South African farmers to Australia
Campaign group AfriForum, which advocates for its largely white membership, many of whom speak Afrikaans, said farmers had been used as "scapegoats" for South Africa's wider problems.
"It must serve as a warning that South Africa runs the risk to lose even more productive, loyal citizens should their concerns about issues such as property rights not be listened to," said AfriForum's deputy chief executive Alana Bailey.
In October 2017 AfriForum put the murder rate for commercial farmers at 156 per 100,000 in 2016-17 -- well above the national average of 34.1 per 100,000.
But independent fact-checking service AfricaCheck warned that it was impossible to definitively state the murder rate for farmers in South Africa.
"South Africa is a very violent society and many people, not just farmers, experience unacceptably high levels of serious crime," Frans Cronje, head of the South African Institute for Race Relations, told AFP.
"It is futile and self-defeating to get into a conflict about whether farmers are more at risk than other South Africans."
Up to 500,000 white South Africans have left the country in the past 30 years, according to official statistics, with Australia ranking as the top destination.
- with AFP