Police and ASIO are scrambling to defuse serious tensions between Australian far-right groups and Islamist extremists, which have reached unprecedented heights in recent weeks with death threats and an apparent attempted murder.

In the most serious case, up to eight gunshots were fired into the Sydney home of a former leader of an anti-Islamic hate group earlier this month.

The former western Sydney president of the Australian Defence League (ADL), Nathan Abela, claims he commando-rolled through his living room to avoid being hit by up to eight bullets fired into his Greystanes home late on April 3.

Police believe the shooting was part of a backlash against the ADL, a registered not-for-profit organisation which incites its followers to violence and has in recent months escalated a vicious hate campaign against Australian Muslims.

The group's members and followers have been stalking and photographing Muslim women on public transport, spraying invective at Muslims on Sydney streets and on social media, displaying anti-Islamic posters outside mosques and even threatening to blow up an Islamic school.

The ADL was established in 2009 as an offshoot of the violent English Defence League, the UK's most provocative street movement in decades.

The Australian group has fewer than 30 paid members, but its Facebook page attracted more than 12,000 followers before it was shut down earlier this month.

The ADL's Facebook presence has since been resurrected with more than 2,000 followers signing up to the new page so far.

One of its leaders is former soldier Ralph Cerminara, an IT technician by day who has spent more than three years as the national president of the ADL and claims to have support from within the Australian Defence Force.

Mr Cerminara told the ABC's 7.30 program the group's aim was to have Islam banned and to "defend Australia's culture and Australia's people at all costs".

A recent post from Mr Cerminara's Facebook account to his followers was even more threatening:

"I am calling for the end of Islam in our country and hopefully the world. "If Muslims have to die then so be it. It is us against them."

In recent weeks, Mr Cerminara ratcheted up tensions with Sydney's Muslim community, urging ADL followers to take photographs of Muslim women in public and post them online.

Several women in hijabs and burqas discovered they had been followed, photographed and subjected to ridicule on Facebook.

A mother of three who was photographed on the morning train to work and then humiliated in a series of vile Facebook posts told 7.30 she has been forced to take stress leave from work and seek counselling for panic attacks.

Mr Cerminara makes no apologies for the personal attacks and public ridicule, telling 7.30: "If that's the way it has to happen, then so be it".

Ralph Cerminara is one of the leaders of the Australian Defence League. ( ABC )

"They are putting that hijab on themselves, the same as a person would be putting a satanic star around their neck," he said.

"We know what they stand for by putting that on."

But Australia's Grand Mufti, Ibrahim Abu Mohamed, says the ADL is trying to "explode society".

"Organisations created in the name of defending Australia want to start a fire in all Australia," he told followers in a recent sermon at Granville Town Hall.

"They deal with the most precious thing a human being has and that is his beliefs."

War of words escalates into shooting

Two months ago, Mr Cerminara expanded the ADL's reach by appointing 24-year-old demolition worker Nathan Abela as the group's western Sydney president.

Abela took to the role with vigour and quickly gained a reputation within Sydney's Muslim community, uploading a series of videos on YouTube of himself preaching, handing out anti-Islamic pamphlets and filming Muslim sites.

It was a video filmed at Australia's biggest Islamic school at Greenacre that rattled the Muslim community and caused police to alert the NSW counter-terrorism squad and ASIO.

In the video posted on YouTube and Facebook, Abela accused the Melek Fahd Islamic School of locking up women. The ADL's Facebook followers suggested the school was a terrorist safe house that should be bombed or burned down.

The actions fuelled an online war of words with Sydney's Muslim extremist community, which escalated in the lead-up to the shooting at Abela's home.

Just days before the shooting, a Sydney man known as Abu Bakr posted a video on YouTube accusing Abela of "making yourself a clear target for the Muslims out there".

"Either you will accept Islam as your salvation, or you will die by the sword," he said in the video, which has since been removed.

Police under pressure to take action

Police are investigating the shooting and continuing death threats against Abela and Mr Cerminara, but have been under pressure from the Muslim community to take action against the Australian Defence League.

NSW Deputy Police Commissioner Nick Kaldas assures a large investigation is continuing into the ADL's actions online and its hate campaign against Muslim women.

"We will not tolerate it and we will be there to do something about it," Mr Kaldas told a community meeting last week.

"There's also some legal advice that we need to get. Some of the offences we can't charge until approval is given by the Attorney-General's Department and that will be pursued."

Late last week, Abela was charged with a number of offences, including trespassing, using a carriage service to menace, harass or offend, and hindering the investigation into the shooting at his house.

The Royal Australian Navy has carried out a separate investigation into the Australian Defence League after reports emerged that some sailors engaged in Operation Sovereign Borders had been posting anti-Islamic comments on social media.

One Navy member who was under investigation had responded to a Facebook post critical of asylum seekers, from someone who claimed to be an ADL member, that he was "about to head out today to deal with these f-----s".

The Navy announced this month that while none of its serving personnel had been found to be members of the ADL, several sailors had been dismissed for inappropriate use of social media.