In a submission to the government's consultations on the religious discrimination laws,they say the new bill must include extra measures to allow them to express their religious identity and feel safe.
"Australians Muslims - and people of minority faiths more generally - need a form of recourse to challenge those who openly vilify them,"they say.
The submission says there have been worrying Islamophobic attacks since the deadly Christchurch mosque shooting earlier this year. It points to theHolland Park Mosque in Brisbane which was vandalised last month with the words"St Tarrant",in reference to the Christchurch shooter,as well as a Nazi swastika.
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It also says harmful content about Muslims has become"mainstream"online.
"[This is] radicalising potentially violent individuals and making it'normal'to attack other Australians in public places because they are readily identifiable as Muslim."
The groups say Muslim Australians do not have the same level of protection as some other religious groups - such as Jewish people and Sikhs - because they get extra protections under the Racial Discrimination Act as ethno-religious communities,from behaviour designed to"offend,insult,humiliate or intimidate".