Australian Prime Minister Tony Abbott on Wednesday ordered an urgent enquiry into why a deranged Islamic gunman was not under surveillance and how he obtained citizenship, as security was stepped up after a fatal cafe siege.

Iranian-born Man Haron Monis, 50, had a history of extremism and violence and was on bail for a string of charges, including sexual offences and abetting the murder of his ex-wife.

Last month he posted a message in Arabic on his website pledging allegiance to "the Caliph of the Muslims", which some have interpreted to mean the Islamic State militant group.

Yet he was allowed to roam free and take 17 hostages at a cafe in the heart of Sydney on Monday, unfurling an Islamic flag during a 16-hour siege which left him and two innocent victims dead. Six others were wounded.

The gunman, whom Abbott called "a madman", was well known to both state and federal police and the domestic spy agency ASIO, but was not on any Australian counter-terrorism watch lists.

"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.

The threshold for placing someone on a watch list boils down to whether they are regarded as being at risk of committing violence against innocent people.

Abbott said the review, due to report in late January, would examine Monis' arrival in Australia from Iran in 1996, the decision to grant him asylum and citizenship, what information agencies had about him and how it was shared.

It would also ask how he managed to get a gun and how he could claim welfare benefits for years despite apparently being able-bodied.

"The system did not adequately deal with this individual. There's no doubt about that, and this is why we've got to constantly learn the lessons of everything that happens," Abbott told a press conference in Canberra.

Police eased an exclusion zone around the scene of the drama in Martin Place after a large swathe of the central business district was shut down as the siege unfolded. But security across Sydney has been stepped up, with hundreds more officers on the streets.

Abbott said he would not rest until he was assured all Australians were safe.

"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 said.

But he added that he would crack down on "people who are preaching hate, associating with terrorist organisations or with terrorist supporters, who are railing against our country and our way of life, our freedoms and our tolerance".

Police Commander Michael Fuller, who is heading Operation Hammerhead, said a ramped-up operation in Sydney was intended to assure the public that "the police are next to them during these difficult periods".

"It's a high-visibility police operation that will focus on putting police out and about in public places, sporting events, transport hubs and other areas that police deem necessary leading up to the busy New Year's Eve period," he added.

Fuller said there had been no intelligence to suggest a repeat of the incident was likely, but "we've all seen the look on the faces down at Martin Place and there is fear".

Fuller revealed there had been some "hate and bias crimes" since the siege but stressed they were isolated and paled in comparison to the outpouring of support for both the victims and the Muslim community.

The siege has touched a nerve among Australians, who began laying flowers at a makeshift memorial in the heart of Sydney's financial quarter on Tuesday. The floral tribute has only grown bigger.

"When you get out into the middle and you're there amongst that emotion, it's overwhelming," said Cat Delaney, who was handing out tissues to mourners.