Omar Al-Kutobi, 24, and Mohammed Kiad, 25, were arrested on Tuesday from their home in Sydney, just hours before the alleged plot to kill someone using a knife was to be carried out.
Police seized a machete, a hunting knife, a homemade flag of the Islamic State militant group and an Arabic-language video detailing the IS-inspired attack planned for that day.
Abbott quoted Al-Kutobi as saying: "I swear to almighty Allah we will carry out the first operation for the soldiers of the caliphate in Australia. I swear to almighty Allah, blond people, there is no room for blame between you and us. We only are you, stabbing the kidneys and striking the necks."
He described the contents of the video as "monstrous extremism".
"I don't think it would be possible to witness uglier fanaticism than this, monstrous extremism than this," he said.
Abbott said Australia needed its security agencies more than ever as it faced an evolving threat.
"Under the influence of the Islamist death cult, all you need to be a terrorist is a knife, a flag, a camera phone and a victim. That's all you need," he said.
"We must defeat this threat and I am confident that this government has the will to do so."
In December, Iranian-born self-styled cleric Man Monis took 18 people hostage for some 16 hours inside a downtown Sydney cafe.
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