Canberra has become increasingly concerned about the prospect of lone-wolf attacks by individuals inspired by groups such as Islamic State, and a tightening of counter- terrorism laws is underway.
Six attacks in Australia have been foiled over the past year, according to the government. But several have not, including a police employee shot dead in Sydney last month by a 15-year-old reportedly shouting religious slogans.
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"I think there can be no doubt that there's a small group in Sydney that are engaged in activity which wants to upset the Australian way of life," he said.
The national broadcaster said the 12 were part of a larger group of 19, seven of whom were in prison.
Some of those under surveillance were subject to orders controlling their movements and communications because police believed there was an "unacceptable, high risk they will commit a terrorist attack", Gaughan added.
"Our first point of call in relation to these investigations is where there's been a criminal offence committed we arrest, charge and prosecute," he said. "If we don't meet that threshold, the next step we look at is a control order."
The revelations came as Turnbull met in Canberra with his national security committee to discuss further ways to deal with violent extremism. He had returned from several overseas summits dominated by terror concerns following the Paris attacks that left 130 dead.
Turnbull told parliament that tackling the financing of terrorism and the use of social media for propaganda, as well as helping build greater social cohesion, were high on his agenda.
"The terrorists want us to bend to their will, to be frightened, to change the way we go about our lives, to abandon our values," he said.
"If we do that, they win. And they will not win, we will not let them win."
A poll in The Australian newspaper showed 76% of 1,573 interviewees believe a terror event in their country is either inevitable, very likely or likely.
Authorities raised Australia's terror threat alert to high just over a year ago. They introduced new security laws and have since conducted several raids.
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