Australia will "in coming days" join ally the United States in an international effort to transport weapons to Kurdish forces fighting IS extremists in northern Iraq.
It has also been conducting humanitarian air drops to the town of Amerli, where thousands of people were trapped for more than two months until Iraqi forces broke the siege on Sunday.
While Abbott has insisted Canberra will not be sending combat troops to the conflict, he has stepped up his rhetoric against the militant group, calling it a "death cult" that is carrying out ethnic cleansing.
On Tuesday he compared them to the Nazis and communists.
"The difficulty here is that these people do exalt in death; they absolutely revel in killing," he told Sydney radio station 2GB.
"We've seen in the century just gone, the most unspeakable things happen, but the atrocities that were committed by the Nazis, by the communists and others, they were ashamed of them, they tried to cover them up.
"This mob, by contrast, as soon as they've done something gruesome and ghastly and unspeakable, they're advertising it on the Internet for all to see which makes them, in my mind, nothing but a death cult.
"That's why I think it's quite proper to respond with extreme force against people like this."
IS has prompted widespread concern as it advances in Syria and Iraq, killing hundreds of people, including in gruesome beheadings and mass executions.
Abbot's comments came as Ban said during a visit to New Zealand that the entire world community should be alarmed at what was happening.
"The situation in Iraq is very worrisome and the activities by IS are totally unacceptable," he said.
"The international community must ensure solidarity. Not a single country or organisation can handle this international terrorism.
"This has global concerns so I appreciate some key countries that have been showing very decisive and determined actions. But all these actions should be supported by all the international community."
The UN chief gave tacit support to plans to airlift arms to Kurdish forces.
"Without addressing this issue through certain means, including some military and counter-terrorist actions, we will just end up allowing these terrorist activities to continue," he said when pressed on the issue.
Australia is gearing up to fly a C-130 aircraft to the Iraqi capital Baghdad for customs clearance "in coming days", before heading to Kurdish-controlled Erbil.
The plane will then reportedly land to hand over weaponry, which will include mortars and rocket-propelled grenades.
The dangers faced by Australian and allied forces were highlighted Tuesday with a report, since denied, that a C-130 Hercules came under machine-gun fire as it dropped aid to Amerli.
"Obviously, flying into a war zone, combat zones, air drops, even humanitarian air drops into combat zones are full of risk, but the risks are reasonable given the importance of the missions they're flying," said Abbott, adding that he was not aware of a plane being targeted.
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You'll have to do better than that to fill the shoes of Tony Blair.