Greens senator Nick McKim labelled Mr Dutton a "racist idiot", sparking a heated exchange with Senator Brandis.
"That is a disgusting thing to say, he ought to be ashamed of himself, he ought to be censured by the Senate," the government leader said Senator McKim welcomed a censure, telling Senator Brandis: "There are opportunities available".
Bill Shorten on Wednesday added to the criticism the immigration minister has faced, saying no-one did more to shape Australia's modern diversity than Malcolm Fraser and Mr Dutton's remarks were profoundly wrong.
Suggesting it was a mistake to allow a generation of migrants to come to Australia because of the crimes of a tiny handful of their grandchildren is not just ignorant and insulting, but a denigration of people who have given so much to the country, he told parliament.
"His ignorant comments contradict and undermine and fly in the face of every briefing I have ever received from our security agencies who explain to us how best to counter radicalisation about defeating extremism" Mr Shorten said.
"Loud, lazy, disrespect, wholesale labelling of entire communities for the actions of a tiny minority, aid and abet the isolation and resentment that the extremists pray upon."
The Labor leader called on the prime minister to show leadership and pull Mr Dutton into line.
'Disgraceful comments against migrant Australians'
Counter-terror expert and Labor MP Anne Aly says she has received threatening emails in the wake of Immigration Minister Peter Dutton's comments about Lebanese Muslim immigration.
Ms Aly said the comments had stoked fear and division and jarred with the prime minister's assertion that an inclusive nation was the best weapon against terrorism.
"If Malcolm Turnbull believes that, if he really believes that, he would have come out and slapped down Peter Dutton's disgraceful comments against migrant Australians who have helped to build this nation," she told reporters in Canberra.
"These are comments that are very typical of the politics of fear and the politics of division, the kind of politics that we really don't need right now in Australia."
The prime minister has thrown his support behind Mr Dutton after he blamed Fraser government immigration policies for problems such as radicalisation and gang violence 30 years on.
Mr Dutton further fuelled the comments in parliament by saying 22 of the past 33 people charged with terrorism-related offences in Australia were from second and third generation Lebanese Muslim backgrounds.
"(Australians) need to ask for a principled leader and they need to have somebody who shows some leadership on this," Ms Aly said.
"Peter Dutton's comments have already started to have impacts around communities."
Ian Macphee, who was immigration minister in the Fraser Liberal government, labelled Mr Dutton's comments "outrageous".
In a statement provided to the ABC by the Refugee Council of Australia, he acknowledged justifiable anger in the community.
"We have had a succession of inadequate immigration ministers in recent years but Dutton is setting the standards even lower," Mr Macphee said.
He described Mr Dutton and One Nation leader Senator Pauline Hanson as "ignorant, alarmist voices".
"The Fraser government honoured international law and morality," he said.
"From the Howard government onwards these have been increasingly discarded."
