One of the hostages held during a siege at an Australian cafe last month was killed by a ricochet of at least one police bullet that also injured three other hostages, an inquest into the deaths was told on Thursday.

Jeremy Gormly, counsel assisting the New South Wales state coroner, said lawyer Katrina Dawson, 38, was hit by six fragments of a police bullet, or bullets, with one striking a major blood vessel.

"She lost consciousness quickly and died shortly afterwards," Gormly said at the opening of the inquest.

Police stormed the Lindt Chocolat Cafe in central Sydney in the early hours of Dec. 16, ending a 17-hour siege by Man Haron Monis after the gunman shot cafe manager Tori Johnson, 34.

Johnson's execution - he was ordered to kneel and then shot without warning at close range in the back of the head - was witnessed by a police marksman, Gormly said.

Monis, 50, who fired 22 rounds from a sawn-off pump action shotgun, was killed instantly by several police bullets and bullet fragments to the head and body, Gormly added.

The inquest is running alongside a government inquiry into how Monis was able to access a gun and why he was granted bail while facing charges as an accessory to the murder of his ex-wife. He was also facing more than 40 sexual assault charges.

The self-styled sheik harboured deep grievances against the Australian government and had found little kinship in the city's large Muslim community, where he was seen as deeply troubled.

He was found guilty in 2012 of sending threatening letters to the families of eight Australian soldiers killed in Afghanistan as a protest against Australia's involvement there.

Gormly said investigators had so far not established any contact between Monis and Islamic State before the siege. There was evidence that a psychiatric profile of Monis "will throw light" on his motivations, he said.

Monis ordered and consumed a piece of chocolate cafe and tea after entering the cafe early on Dec. 15, the inquest heard. Around half an hour later, he asked to move tables and to speak to manager Johnson, who then asked an employee to lock the doors. Once that was done, Monis stood up, putting on a vest and bandana, telling staff, according to one hostage account: "This is an attack. I have a bomb."

Coroner Michael Barnes said he would conduct the inquiry as quickly as possible, noting it raised "issues relevant to the actual security and the sense of security of the wider population".