Delivering his maiden speech on Tuesday, Fraser Anning called for a ban on all further Muslimimmigration and invoked the words "final solution" - the term referring to the Nazi extermination of millions of Jews - when calling for a popular vote on immigration.
Later on Wednesday Hanson introduced her private member's bill "to give voters a say on whether Australia's immigration levels are too high by casting a vote at the next general election".
Anning, in his first speech to Parliament, called for a return to the country's historic "White Australia" policy that explicitly favored immigration by Europeans over Asians and Pacific islanders.
Mr Anning joined Parliament past year as a One Nation senator but has since defected to Katter's Australian Party.
"While all Muslims are not terrorists, certainly all terrorists these days are Muslims, so why would anyone want to bring more of them here?" he asked.
A member of the minor Katter's Australian Party, Anning was unapologetic about using the same phrase Nazi leaders used in planning the Holocaust during World War II. Anning was elected on the One Nation ticket before switching to Katter's Australian Party. "We reject and condemn racism in any form", he said on Twitter.
The speech has sparked outrage across the political spectrum. At that time, ensuring the "final solution" (Endlosung) of the so-called "Jewish question" was the backbone of the Third Reich's actions on occupied lands. "I want to apologise to the Senate and the Australian people that after the vomitous poison last night I then, stupidly, and unthinkingly, and I did think about it, I followed Senate protocol and I should have lined up here and shook this unworthy man's hand", a clearly emotional Hinch said.
"I am Muslim migrant, I'm about to be a Senator and there's not a damn thing Fraser Anning can do about it", she wrote in a piece for a website.
Prime Minister Malcolm Turnbull described Senator Anning's remarks as "appalling" and said there was "no place in Australia for racism".
Senator Anning refused to apologise for his comments during an interview with Channel 9's Today Show on Wednesday morning, he also walked out of the chamber as Labor Senator Penny Wong moved a motion condemning the speech.
Derryn Hinch, an opposition MP, called Anning "Pauline Hanson on steroids".
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.
"It was never meant to denigrate the Jewish community and it's two words and if that offends anyone, unfortunately, that's the way it has to be".
However, hitting back at the criticism, Bob Katter, the leader of Anning's party, KAP, said he supported his colleague's statement "1,000 per cent". "This might go some way to helping encourage others like me to put their hand up and make parliaments look a bit more like the streets and suburbs of the country we live in".
In a speech, Mr Dutton also called out Senator Anning's views on Wednesday.