The Queenslander was rebuked by his colleagues on Wednesday for blaming Muslim migrants for the horrific attack last month in which a white supremacist killed 50 worshippers at mosques.

"Senator Anning's comments were ugly and divisive. They were dangerous and unacceptable from anyone, let alone a member of this place," government Senate leader Mathias Cormann told parliament.

Labor's Senate leader Penny Wong said while scores of injured people were being treated for gunshot wounds, Senator Anning fanned the flames of division.

"How pathetic. How shameful. A shameful and pathetic attempt by a bloke who has never been elected to get attention by exploiting diversity as a fault line for political advantage," she said, without mentioning Anning's name.

The censure came as the Australian Electoral Commission official registered "Fraser Anning's Conservative National Party", giving the senator a better chance of retaining his seat than if he ran as an independent.

Objections from the Australian Conservatives and the Nationals about name confusion were not upheld.

Senator Anning originally stood for One nation and entered parliament after the party's Malcolm Roberts was disqualified for being a dual citizen.

He was widely condemned for a series of racist comments including a reference to the "final solution" - a Nazi term - in his first speech to parliament.

Senator Anning said he had pointed out that New Zealand's immigration policy allowed radical Muslims into their country, which helped cause the massacres.

"My real crime is that I simply told the truth at a time when the left-wing political and media elites least wanted to hear it," he said.

Senator Anning was branded a "disgrace" for saying Sudanese and Muslim migrants had a proven track record of causing crime and terrorism in Australia.

"It is an established fact that diversity undermines cohesion, increases alienation and is a key driver of increasing crime," the senator said.

Greens leader Richard Di Natale said he wanted to focus on addressing hate speech in society, only making brief mention of Senator Anning.

"He has shown himself to be a pathetic man lacking any empathy," he said.

But the Greens' bid to suspend Senator Anning from parliament for the rest of the final sitting day of the year in the upper house failed.

One Nation's Peter Georgiou read a speech on behalf of party leader Pauline Hanson, saying they would abstain from the "public flogging" of the censure motion.

No senator voted against the part of the motion which censured Senator Anning.

While Senator Anning won just 19 below-the-line votes at the 2016 election, 250,000 Queenslanders supported the One Nation ticket he was on.

After a falling out with Pauline Hanson and later Bob Katter, he split with their parties to sit on the crossbench.

Australian Associated Press