The prime minister wants independent senator Fraser Anning to face "the full force of the law" over his comments the Islamic community was to blame for the New Zealand mosque massacre.
And New Zealand's representative in Australia says the Queensland senator's comments were atrocious.
The government and Labor are planning a bipartisan motion condemning Senator Anning when parliament returns in April.
However, Scott Morrison went further on Sunday, when asked if a parliamentary motion was enough, saying: "I think the full force of the law should be applied to Senator Anning."
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He previously said the comments the senator made were appalling, ugly and had no place in Australia.
New Zealand High Commissioner Annette King said her country rejected absolutely Senator Anning's sentiment.
"We just condemn what he said and I'm absolutely delighted that his comments were condemned from the very top of government here in Australia and the people of Australia," she told reporters in Canberra..
However, she said it was up to Australians to decide if he was fit to be an elected representative.
A change.org petition calling for Mr Anning's expulsion from parliament has amassed almost 750,000 signatures.
"We call on the Australian government to expel this man who blames victims for their own violent deaths, and uses references to genocide to further his hateful agenda," it states.
A 17-year-old boy was arrested after allegedly throwing an egg at Senator Anning at a speaking event at Moorabbin in Melbourne on Saturday.
