Australian Prime Minister Tony Abbott on Tuesday warned of heightened "terrorist chatter" in the aftermath of the fatal Sydney cafe siege and said another attack was likely, as tearful mourners paid tribute to the victims.

Iranian-born gunman Man Haron Monis, who had a history of extremism and violence, took 17 hostages in the city's financial heartland last week, unveiling an Islamic flag and demanding to talk to Abbott.

He was killed as armed police stormed the eatery after 16 hours. Two hostages also died -- mother-of-three Katrina Dawson, 38, and 34-year-old Lindt cafe manager Tori Johnson -- while several were injured.

"A briefing from the security agencies today indicated that there has been a heightened level of terrorist chatter in the aftermath of the Martin Place siege," Abbott said after a meeting of his National Security Committee.

"That's why it's important that people remain alert and aware as well as reassured that our police and security agencies are doing everything they humanly can to keep us safe."

Abbott did not raise Australia's terror alert level beyond its current high, which means an attack is likely. An extreme alert level means one is imminent or has occurred.

"I am alerting people to the fact that the terror threat remains high and as you all understand, at this level, an attack is likely," he said.

Australia raised its threat level to high in September when it carried out a series of counter-terrorism raids across Sydney and Brisbane following a flow of its nationals to Iraq and Syria to fight with the Islamic State group and other jihadists.

At that time, Abbott said the raised threat was not prompted by a specific attack plan but a "body of evidence that points to the increased likelihood of a terrorist attack in Australia".

Australia has not officially branded the Sydney seige as a terrorist attack and Abbott said "I'm not going to speculate" on any potential new threat.


'Emotions still raw'

The warning comes as emotions remain raw over the siege, which triggered an outpouring of grief that saw thousands of bouquets laid at a makeshift memorial near the cafe in Martin Place that has grown bigger by the day.

A week after the tragedy -- and with storms forecast in New South Wales -- state Premier Mike Baird said the time was now right to clear the area, with an army of Red Cross workers, volunteers and council officials moving in Tuesday.

They respectfully collected the flowers, most of which will be used at a suitable site after consultation with the victim's families, while the countless notes, messages and cards will also be preserved.

"At an appropriate time, we'll also discuss with them (the families) the establishment of a permanent memorial," Baird said.

A private funeral was held Tuesday for Johnson -- hailed a hero after reportedly trying to wrestle the gun from Monis -- with hundreds of tearful mourners at St Stephen's Uniting Church just metres from where he died. Several of the hostages also attended.

The service emphasised unity after the attack, with the Johnson family using a phrase by Persian poet Rumi on the front-page of the order of service: "Out beyond ideas of wrong-doing and right-doing, there is a field. I will meet you there."

A memorial for lawyer Dawson also took place at Sydney University's Great Hall with up to 1,000 mourners, including Abbott, wearing black with splashes of aqua -- her favourite colour.

In emotional speeches, Dawson's family and friends fought back tears as they spoke of her intelligence, generous spirit and deep love for her children.

"She was destined to change the world, just not the way it's happened," her older brother Sandy Dawson said.

Monis, who was known to authorities, was on bail at the time for a string of charges, including sexual offences and abetting the murder of his ex-wife.

Abbott has ordered an urgent inquiry into the circumstances surrounding the siege.