In a national security address yesterday, Abbott said he had often heard Western leaders describe Islam as a "religion of peace" and that he wished Muslim leaders "would say that more often, and mean it".
"Everybody, including Muslim community leaders, needs to speak up clearly because, no matter what the grievance, violence against innocents must surely be a blasphemy against all religion," he said.
The Islamic Council of Victoria, which represents that state's more than 150,000 Muslims, said it was one of many community bodies which had repeatedly condemned all forms of violence and extremism.
"The PM's lack of acknowledgement or appreciation of Muslim community leaders and members who volunteer their time to consult with all levels of government and enforcement agencies misleads and incites ill-feeling from the broader community."
The council urged other community organisations to pressure Abbott to promote national unity and "cease scapegoating one segment of our society".
Abbott, who has termed the brutal Islamic State jihadist group in Iraq and Syria a "death cult", insisted Tuesday he was thrilled more Muslim leaders were speaking out against violence.
"It is not enough to say the right thing, you have got to mean the right thing and sometimes government has got to enforce doing the right thing."
A string of incidents, including a December siege in a Sydney cafe by a self-styled cleric who attempted to link his actions to Islamic State, have raised awareness about radicalisation among Muslims in Australia.
