Opening a summit on countering violent extremism in Sydney, Abbott said the Islamic State terror group could not be negotiated with, only fought.
"We are talking with our friends and partners about how the air strikes might be more effective and how the Iraqi forces might be better helped," he said, adding "this is terrorism with global ambitions".
He said IS holds sway over an area as large as Italy in eastern Syria and northern and western Iraq, while its affiliates control parts of Libya and Nigeria.
"The tentacles of the death cult have extended even here as we discovered with the Martin Place siege last December," Abbott said.
He said in the past year IS and its imitators carried out attacks in Sydney and in Melbourne, as well as in France, Belgium, Canada, Afghanistan, Pakistan, Egypt, Nigeria, Jordan, Denmark, Kenya and the United States.
"You can't negotiate with an entity like this, you can only fight it," he said.
Australia is the second-largest single contributor to the fight against IS in Iraq, providing 300 trainers based in Taji, an air task group and special forces on a counter-terrorism advise-and-assist mission in western Anbar.
"At home, we are trying to ensure that Australians don't leave this country to join the 15,000 foreign fighters already in Syria and Iraq. Counter-terrorist units from the Australian Border Force are now operational at all our international airports," Abbott said.
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