It would be an offence to possess "instructional terrorist material" and to make terrorism hoaxes under new laws to be considered by state and federal leaders at a special terrorism-focused Council of Australian Government meeting in Canberra on Thursday.
The two new offences, outlined in a leaked copy of the meeting's agenda obtained by Fairfax Media, are among a broad range of counter-terrorism issues that will be examined at the special meeting.
These include an updated national counter-terrorism plan, "better equipping our agencies to prevent and respond to terrorist incidents", including through a national facial biometric matching capability, and enhancing the existing national pre-charge detention regime.
The government wants the states to introduce a nationally consistent approach to bail and parole for terror suspects; a measure it first flagged in June.
The leaked agenda, marked "for official use only", reveals the government plans to enhance Defence's ability to support the states and territories' "response capabilities" to terror incidents.
Prime Minister Malcolm Turnbull announced the special summit back in June and promised at the time the it would "comprehensively review our nation's laws and practices which are directed at protecting Australians from violent extremism".
Under current Australian laws, it is already an offence to commit a terrorist act, plan or prepare for a terrorist act, finance terrorism or a terrorist, provide or receive training connected with terrorist acts, possess things connected with terrorist acts or to collect or make documents likely to facilitate terrorist acts.
The meeting on Thursday will take place just three days after the massacre of at least 59 people by a gunman in Las Vegas, an incident Mr Turnbull said on Tuesday was a "brutal and callous killing; completely senseless".
Mr Turnbull declined to comment on whether the United States should adopt tougher gun laws following the latest in a string of mass shootings, as Australia did after the Port Arthur massacre in 1996.
"I just simply say this; we are very, very proud of our strict gun control regime in Australia. We maintain it, we are not complacent about it at all, as indicated by the recent amnesty and its effectiveness and we will continue to police it," he said.
Ahead of Thursday's COAG meeting, Mr Turnbull said the first duty of every government is to keep its citizens safe and, to that end, he had called the meeting with state and territory leaders "to further advance and harmonise our response to the threat of terrorism".
"A little over a month ago, we released our National Crowded Places Strategy - a very important piece of work, a collaborative piece of work, which I commissioned last year after the Nice truck attack to ensure that we had the high standards in terms of protecting crowded places, places of mass gathering, stadiums, concerts and so forth.
"We have to be relentless. There is absolutely no place for 'set and forget' when it comes to national security."
Aviation security measures and the recently announced "Strategy for Protecting Crowded Places from Terrorism" will also be discussed at Thursday's meeting.
The national Strategy for Protecting Crowded Places from Terrorism gives detailed advice to owners and operators of places that attract crowds on how to cut the risk of car and truck attacks, homemade bombs, knife and gun assaults and chemical attacks.