"We need a plebiscite to allow the Australian people to decide whether they want wholesale non-English speaking immigrants from the third world, and particularly whether they want any Muslims, or whether they want to return to the predominately European immigration policy..."
The reasons for ending all further Muslim immigration "are both compelling and self-evident", Anning said, before claiming that a national referendum on the "problem" was the "final solution".
A member of the Australian Party, Mr Anning was unapologetic about using the same phrase Nazi leaders used in planning the Holocaust during the Second World War.
"No matter how much I brush it aside, it does take its toll", she said.
Crossbench senator Derryn Hinch was sitting in the Upper House listening to the speech and said it was excruciating. 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".
The non-apology was followed up with an appearance on Sydney's 2GB Radio, where he told host Alan Jones that Muslim immigration needed to end because some of the immigrants could be terrorists.
Mr Katter said he genuinely believed Mr Anning had no idea of the historical context of the term.
Australian senator Pauline Hanson reacts as she talks with local Aboriginal people in the northern Australian town of Rockhampton in Queensland, Australia, November 8, 2017.
"To describe the so-called safe schools and gender fluidity garbage being peddled in schools as cultural Marxism is not a throwaway line, but a literal truth", Senator Anning said.
"That has nothing to do with "the final solution", the thought police got onto that".
Calling for a new immigration policy that promotes "European Christian" values, Anning declared: "We as a nation are entitled to insist that those who are allowed to come here predominantly reflect the historic European-Christian composition of Australian society".
In her speech in the NSW parliament, Faruqi recalled enduring racist and sexist trolling during her tenure as MP "not because of what I'm doing but because of who I am, where I come from, and the colour of my skin".
Mehreen Faruqi has joined Australia's senate as its first female Muslim member, on a day the country is caught up in a bitter row over racism.
Anning also called for a complete ban of Muslim immigration, stating his reasoning as a perceived link between Muslim communities and terrorist activity.
Greens leader Richard Di Natale, on the other hand, called Anning's comments as "vile", demanding an apology from him.
Home Affairs Minister Peter Dutton told Parliament he strongly supported the motion moved by Labor to condemn racism.