Abbott's comments came after police detained 15 people in the biggest counter-terrorism raids across the country early Thursday, Xinhua reported.
Abbott said that a senior member of the IS, who is an Australian, had urged supporters at home to carry out "demonstration killings" in Australia.
More than 800 police officers conducted searches at 25 places across Sydney on a group of people who allegedly had "intented to carry out random attacks on individuals in Australia", Xinhua reported.
A man was charged with "serious terrorism-related offences" and will appear in a Sydney court later Thursday.
In Sydney, police said they believe the group was actively preparing for attacks. However, there is no information regarding a specific attack, including dates, time or location.
Police said the searches were undertaken to prevent the group's activities at the earliest opportunity, and collect further evidence.