The Sydney Morning Herald newspaper reported that Mr Anning had "the most inflammatory maiden speech to an Australian parliament" since Ms Hanson said in 1998 that Australia was "in danger of being swamped by Asians".
Anning, formerly of One Nation but now with the Katter's Australian Party, attracted instant backlash for using the phrase "final solution" in regards to immigration.
"I call on Fraser Anning not only to apologise but also to go and visit a Holocaust museum and to hear first hand from the survivors how the pain is still raw", he told Sky News on Wednesday.
He added: "The final solution to the immigration problem is, of course, a popular vote".
But Mr Katter called it a magnificent speech that he supported "a thousand per cent".
Labor opposition leader Bill Shorten called the speech "a low point for our parliament".
"I am appalled by Fraser Anning's speech".
In that speech he used the phrase "final solution", which was the phrase used by the Nazis under Adolf Hitler which meant annihilating Jewish people from Europe.
"We do not want people coming in from the Middle East or North Africa unless they're the persecuted minorities", Mr Katter said.
The Justice Party senator had been condemned for shaking Anning's hand after the speech, as it is custom for senators present in the chamber to do, but on Wednesday he said he regretted doing so. "That has nothing to do with the 'Final Solution, ' the thought police got onto that".
"If people want to take it out of context that's entirely up to them", he told Nine Network.
"It was never meant to denigrate the Jewish community, it is two words and if that offends anyone unfortunately that is the way it has to be".
In his maiden speech at the Senate on Tuesday, Anning targeted global students by asking for an "end to Australian-job-stealing 457 visas" and "force worldwide students to return to their country of origin once they finish their education".
"He makes it easier for the speech that we heard [on Tuesday]". Hanson said she warned Anning not to take Howard on to his staff when Anning replaced Roberts after his disqualification.
The Greens moved a motion in the Upper House to censure Mr Anning over his comments, but it did not get enough support to pass.
On the floor of Parliament, MPs of all stripes strongly repudiated Senator Anning's remarks.
He also sparked widespread anger by urging a ban on Muslim migrants and defending the race-based White Australia immigration policy that was in place for seven decades from 1901.
Shorten said parliament couldn't remain silent when it comes to racism.
On Wednesday, the Senate considered a motion noting Australia had benefited since the dismantling of the White Australia discriminatory immigration policy in 1973, where many senators pointedly slammed Anning.
Other political leaders spoke out, including Anne Aly, Australia's first Muslim MP. She said he then asked for a position in her office but she refused.
"I'm exhausted of having to stand up against against vilification, time and time and time again".