Following the backlash, Senator Anning has continued to defend his comments.
The 28-year-old Australian, identified as Brenton Harrison Tarrant, killed 49 people and injured 48 others after he opened fire at two mosques in Christchurch on Friday.
"Whilst this kind of violent vigilantism can never be justified, what it highlights is the growing fear within our community, both in Australia and New Zealand, of the increasing Muslim presence", he wrote.
Opposition Leader Bill Shorten, who labelled Senator Anning's comments as "disgusting", said Labor would support a parliamentary censure motion of the "rogue" Queensland senator.
Dr Jneid urged all governments to give extra attention to the rise of anti-Muslim sentiment and extremism and also encouraged all mosques and places of worship and Muslims in Australia to be extra vigilant in the coming days.
"Those views have no place in Australia, let alone the Australian Parliament", Morrison tweeted.
"It's sad that things have got to get to a point where this white supremacist's hate speech is said in our own Parliament", Aly said.
Canadian singer Bryan Adams cancels concert following mass shooting at Christchurch mosques
At least 49 people were killed at mosques full of worshippers attending Friday prayers in Christchurch . Health officials said 48 other people were being treated at Christchurch Hospital for gunshot wounds.
'Australians will be utterly ashamed of this racist man.
Pakistan's Federal Minister for Human Rights Shireen Mazari also criticised the anti-Muslim remarks, saying that this mindset encouraged anti-Muslim terrorism.
Anning's entire persona was born of Islamophobia, and almost every tweet and speech he makes contains anti-Muslim tirades.
Independent Queensland Senator Fraser Anning has been slammed for his appalling response to the Christchurch terror attack.
"I hope there is a real question as to his position as a federal parliamentarian given the privileges and the responsibilities which are attached to that".
Amid the controversy, an unnamed young man slapped an egg on the back of Anning's head during a news conference in Melbourne, prompting the senator to hit him in the face repeatedly before being stopped by what appeared to be a security guard.
Even that message of his had brought considerable backlash from Twitteratis who said it was in fact he who needed to be out of the parliament.