In a post on the Katter's Australian Party page, the party said Anning was "under attack for speaking the truth" and that he needed support so he could "fulfil his promise to reduce immigration levels and take back Australia from the extremists".
"Labor frontbencher Chris Bowen said the use of the term 'final solution", which has been historically associated with the Nazi plan in World War II for killing millions of Jews, was "utterly unacceptable".
One Nation leader Pauline Hanson - whose infamous maiden speech in 1996 was dubbed racist for warning the country was in danger of being "swamped by Asians" - also joined the widespread condemnation of Senator Anning on Wednesday, saying she was "appalled" by the speech. "Australia is a warm and open nation".
"I'm find with what I said and I'll stand by it".
The embattled Queensland representative was originally elected as a replacement for a senator from Pauline Hanson's nationalist One Nation party, but chose to sit as an independent before switching his allegiance to Katter in June this year. He called for the government to ban all welfare payments to migrants in the first five years of living in Australia, labelling many asylum seekers as "welfare seekers".
"I think we could all be a more aware of the sustained abuse that some of us have to weather".
Amid national outrage Turnbull, who will head to the polls within nine months, quickly condemned Anning.
He descried the use of loaded terms, which Senator Anning says were taken out of context, as a "shocking insult" to Australian Jews and Holocaust survivors.
He effectively called for a return to the White Australia policy, where most migrants would be from a European Christian background.
The Greens called on Mr Katter to expel the Queenslander from his party, with leader Richard Di Natale calling Senator Anning "a myopic red-neck reaching out from another time to another people". "But unfortunately if you have a jar of jelly beans and three of them are poisonous, you're not going to try any of them", he told Alan Jones of radio 2GB, while referring to Muslims. "That has nothing to do with the 'Final Solution.' The thought police got onto that".
"I believe that the reasons for ending all further Muslim immigration are both compelling and self-evident", he said.
"So we reject, we condemn racism in any form, and the remarks by Senator Anning are justly condemned and rejected by us all", he said.
There has been a hugely negative response to his speech in the hours since it was made..
Guardian Australia contacted Anning and Howard for comment.
"Senator Cormann, like others, followed usual Senate practice after every first speech", she said.
In her leaving speech to the NSW parliament on Tuesday, she spoke about enduring "toxic, racist and sexist trolling" in her time as an MP "not because of what I'm doing but because of who I am, where I come from, and the colour of my skin".
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