SYDNEY (AFP) - Australian Prime Minister Tony Abbott vowed on Wednesday not to rest until he was assured Australians were safe, as he formally announced a review into the fatal Sydney cafe siege.

"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 Martin Place siege and how the lone 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."

In the incident on Monday, gunman Man Haron Monis held up the Lindt Chocolate Cafe for 16 hours.

Mr Abbott earlier vowed a transparent probe into why 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 the 17 hostages dead.

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," Mr Abbott said.

The inquiry will be undertaken by federal and state officials, and is expected to report back by the end of January.

Other issues the reveiw would focus on would include: How he got his Australian permanent residency, why he was set free on bail, why he had been taken off the terrorism watchlist in 2009 and why he was getting welfare payments, reported the Sydney Morning Herald (SMH).

The Iran-born Monis was convicted last year of sending offensive letters to families of soldiers killed in Afghanistan and faced charges of being an accessory to the murder last year of his former wife. He also faced several charges of sexual and indecent assault stemming from his work as a "spiritual healer".

However, he was allowed to be released on bail, and was on bail at the time of the siege.

Monis was well known to intelligence agencies and police, Mr Abbott had earlier said, noting that he was not on a terrorism watch list.

"How can someone who has had such a long and chequered history not be on the appropriate watch lists and how can someone like that be entirely at large in the community?" he said at an earlier press conference. "These are questions that we need to look at carefully and calmly and methodically."