A petition to have Australian Senator Fraser Anning booted out of the country's parliament has attracted more than 715,000 signatures.

Anning, an independent Senator from Queensland caused outrage when he blamed the Christchurch shootings on "the immigration program that allowed Muslim fanatics to migrate to New Zealand in the first place".

The only person charged in relation to the attack so far is an Australian man with extreme far-right views, according to a manifesto he posted online before allegedly carrying out the attack.

A petition on change.org started by Kate Ahmed says he "has no place in the government of our democratic and multicultural country".

"We request that he be expelled from his position as Senator, and investigated by law enforcement agencies for supporting right wing terrorism."

Anning, who has previously called for a "final solution" in dealing with immigration, punched a teenager in the head when confronted about the controversial comments about Christchurch.

On Saturday, while speaking to media in Melbourne, Anning had his head slapped with an egg, before turning around and punching the young man who did it - William Connolly - twice. The boy was then set upon by Anning's supporters.