Australian Prime Minister Tony Abbott has questioned why the gunman in the Sydney cafe siege was not on the country's terror watch list.
He said the government would examine why Man Haron Monis had been on bail.
Mr Abbott paid tribute to the two hostages who died in Monday's siege, describing them as "good people".
The two hostages and Monis died as police commandos stormed the cafe in Martin Place early on Tuesday morning, ending the 16-hour siege.
An investigation has been launched into the police operation.
Police are also investigating the motives of Monis - an Iranian refugee who faced multiple criminal charges - and how he got a gun.
At a press conference, Mr Abbott said: "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.
"These are questions that we need to look at carefully."
However, he added that it was "possible" that the siege would have taken place even if Monis had been on a watch list.
"The level of control that would be necessary to prevent people from going about their daily life would be very, very high indeed," he said.
The victims have been named as cafe manager Tori Johnson, 34 and Sydney lawyer Katrina Dawson, 38.
In Martin Place, people have been arriving to sign condolence books and leave flowers in their memory.
Analysis: Frank Gardner, BBC Security Correspondent
From Woolwich to Ottawa and now to Sydney, there is a growing list of individuals carrying out attacks in the name of global jihadism yet apparently unconnected to any organisation or co-ordinated plot.
Rarely are the perpetrators unknown to the authorities. Monis was a known extremist facing criminal charges. Michael Adebolajo, one of the two Woolwich murderers in 2013, was also a known extremist who had been imprisoned in Kenya.
So why were these men allowed to wander around cities, free to pick up knives or guns? The answer comes down to priorities. In open democracies, police and intelligence services do not have the manpower and resources to follow every suspect on their lists around the clock. Inevitably they have to prioritise from an ever-changing list.
A radicalising event such as civilians being killed in a drone strike somewhere in the world can draw more people towards a course of violent action. Often that person may keep their thoughts to themselves and not communicate them in ways that can be tracked.
In an age of so-called "lone wolf" attacks, prioritising suspects is an area the authorities in many countries are going to need to get better at.
Four other people, including a police officer, were injured. The officer has been discharged, while the other three were in a stable condition, police said.
Central Sydney was put in lockdown on Monday morning as the gunman entered the Lindt Chocolat Cafe and seized 17 hostages.
Five hostages managed to sprint to safety on Monday afternoon. Several more escaped early on Tuesday, as commandos stormed the cafe.
How the 16-hour Sydney siege unfolded
- 1. At 09:45 on Monday local time (22:45 GMT Sunday) police are called to the Lindt Chocolat Cafe in Sydney following reports of an armed robbery. It soon emerges a gunman is holding a number of people hostage.
- 2. Between 16:00-17:00, three men, then two women, sprint to safety from the cafe's side door - a fire exit.
- 3. Just after 02:00 on Tuesday, a loud bang is heard from the cafe and special operations officers advance towards the side door.
- 4. More hostages escape, running to safety on Elizabeth Street.
- 5. Moments later, commandos storm the cafe via a number of entrances. The remaining hostages escape.
- 6. Police officially confirm the end of the siege at 02:45 local time. They later report the deaths of three people, including the gunman.
At a news conference on Tuesday, NSW Police Deputy Commissioner Catherine Burn would not say whether Monis had shot the two hostages himself.
Nor would she confirm reports that Mr Johnson was shot when he grappled with Monis. But she said all the hostages had "acted courageously".
Asked why police stormed the cafe, Commissioner Burn would say only that "shots were heard and an emergency action plan was activated".
She said it was "extremely important" she did not comment on events in detail while the investigation is under way.
On Tuesday evening, a crime scene perimeter remained up around the cafe, but police said all roads would be re-opened by Wednesday morning.
Police have promised more officers on the street for the next three weeks.
At the scene: Wendy Frew, BBC News Online, Australia editor
At Christmas time in Sydney, people come to Martin Place to see the giant Christmas tree. This year they have come to see a sea of flowers laid in memory of the victims of this week's cafe shooting.
Hundreds of bouquets have been laid on the pedestrian plaza a block away from where the siege took place.
Well-wishers like Maureen Sharma and Ruza Fisher have come to sign a condolence book and to lay flowers. The two young office employees who work nearby wanted to pay their respects.
"I came to work this morning and could not stop crying," said Ms Sharma. "It touched me more than I had expected." Ms Fisher said her stomach was in knots. "I am starting to well up… It was such a waste of lives."
Monis, a self-styled Muslim cleric, sought asylum in Australia in 1996. He had a history of religiously inspired activism, but officials say there is as yet no evidence his actions were linked to international Islamist movements.
He was convicted of sending offensive letters to the families of deceased Australian soldiers in 2009.
In 2013, he was charged with being an accessory to the murder of his ex-wife, and given bail.
He also faced more than 40 sexual and indecent assault charges.
Monis had "vehemently denied" the assault and accessory to murder charges, his former lawyer told the BBC.
He "believed he was being victimised" for his "lobbying against the government", and had alleged that he was tortured while in custody, Manny Conditsis said.
According to Australian media, a High Court had dismissed Monis' appeal against his previous convictions on Friday.
A church service was held at Sydney's St Mary Cathedral on Tuesday to mourn the victims.
Archbishop Anthony Fisher said the "heart of our city is broken by the deaths of two innocents", and urged Australians not to be caught up in "violence and its cycle of recrimination".
The Australian National Imams Council issued a statement saying it was "deeply saddened by the tragic end to the siege with the loss of life.
"Our thoughts and prayers go out to the families of those killed and to the hostages who suffered the trauma of the siege."