Abbott says will not rest till Australians safe as possible

"I will not rest until I am confident that you are as safe as any government can possibly make you," he said in confirming an official probe into the tragedy and how the Iranian-born Islamist gunman gained citizenship.

"I don't want people who are perfectly good Australians to be frightened of a knock on the door in the middle of the night. That's the last thing that I would want," he added.

"But people who are preaching hate, who are associating with terrorist organisations or with terrorist supporters, who are railing against our country and our way of life, our freedoms and our tolerance, and the welcome that we give to people... these are things which to need to be questioned."

Abbott earlier vowed a transparent probe into why gunman Man Haron Monis, 50, was not under surveillance given he was a known extremist and had a dubious past record.

He said an urgent review would look at what lessons could be learned from events leading up to and surrounding the siege, which left Monis and two of 17 hostages dead.

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It will examine the circumstances surrounding Monis' arrival in Australia from Iran and subsequent granting of asylum and citizenship, and what information agencies had about him and how it was shared.

It will also ask how he managed to get a gun.

"I certainly want answers to those sorts of questions and there was incredulity around the National Security Committee of the Cabinet yesterday when we were briefed on the details of his record," Abbott said.