Anning has shrugged off the criticism over his use of the phrase "final solution" during his maiden speech.
Meanwhile, rival party leader Katter said he stood by Anning's speech "1,000%".
"His speech was absolutely magnificent and it's everything that this country should be doing", he said.
Mr Anning, a northern Queensland hotelier, called for a nationwide vote to decide whether Australians wanted "wholesale non-English speaking immigrants from the third world".
"He didn't get to a university to know the significance of all these words", Katter said. If people want to take it of context that is entirely up to them. "It was never meant to denigrade the Jewish community", he said.
Other senators said they regretted shaking Senator Anning's hand following his first speech, as is general protocol. "The speech was written by a Richard Howard, straight from [Joseph] Goebbels' handbook from Nazi Germany", she said.
Fraser Anning, who is the only member of the federal Senate from the far-right Katter's Australian Party.
"I think the safest thing for Australia is that we don't have any more of them coming into the place".
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.
"How gutless are members in this Parliament?"
"We as a race of people are being buried by a mass migration program to line the pockets of the rich and powerful in Sydney", Mr Katter said.
Anning, who has been in parliament for less than a year has entered into a lose alliance with several conservative independent lawmakers that has boosted his otherwise inconsequential role in Australia's upper house.
More than 20 senators, including senior government ministers, shook hands with Senator Anning after his speech on Tuesday.
"The vast majority of the victims of Islamist terrorism are Muslims", Mr Turnbull said.
"Those who seek to demonise all Muslims on the basis of the crimes of a tiny minority are helping the terrorists", PM Malcolm Turnbull said. I'll be very clear about this.
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.
Energy and Environment Minister Josh Frydenberg, whose mother was a Hungarian refugee who escaped the Holocaust, demanded Senator Anning immediately retract the "ignorant and insensitive" remarks. "We should condemn, as we have, racism and discrimination of the kind so regrettably, so shamefully expressed by senator Anning". "All of us unite together to fight against the scourge of racism - we always have and we always will", he said.
Ms Aly told Parliament she was proud of the response from all sides of politics against Mr Anning's speech.