Australian authorities have carried out their largest "counter-terrorism" raids so far, detaining 15 people to stop an alleged plot by supporters of the Islamic State of Iraq and the Levant (ISIL) to carry out "demonstration killings" in public.

A pre-dawn operation was carried out on Thursday across Sydney and Brisbane by more than 800 officers acting on about 25 search warrants.

The raids came in response to intelligence that an ISIL leader in the Middle East was calling on Australian supporters to kill, Prime Minister Tony Abbott said.

Abbott was asked about reports that the detainees were planning to behead a random person in Sydney.

"That's the intelligence we received," he told reporters. "The exhortations - quite direct exhortations - were coming from an Australian who is apparently quite senior in ISIL to networks of support back in Australia to conduct demonstration killings here in this country."

Police were holding six people and have identified the suspected ringleader, officials said. Nine other people were detained but were freed before the day was over.

Terror alert

The raids came barely a week after Australia boosted the terror threat level to "high" for the first time in a decade, on growing concern about armed members of ISIL returning from fighting in Iraq and Syria.

Attorney General George Brandis confirmed that a person born in Afghanistan who had spent time in Australia and is now working with ISIL in the Middle East ordered supporters in Australia to behead people and videotape the killings.

"If the ... police had not acted today, there is a likelihood that this would have happened,'' Brandis told the Australian Broadcasting Corp.

The Australian government believes up to 60 Australians are fighting alongside ISIL, while another 100 were actively working to support the movement at home.

Mohammad Ali Baryalei, who is believed to be Australia's most senior member of ISIL, was named as a co-conspirator in court documents filed on Thursday.

Police have issued an arrest warrant for Baryalei, a 33-year-old former Sydney nightclub bouncer.

One of those detained, 22-year-old Omarjan Azari of Sydney, appeared briefly in a Sydney court on Thursday.

Prosecutor Michael Allnutt said Azari was involved in a plan to "gruesomely" kill a randomly selected person - something that was "clearly designed to shock and horrify" the public. That plan involved an "unusual level of fanaticism," he said.

Azari is charged with conspiracy to prepare for a terrorist attack.

In court documents, Azari is accused of conspiring with Baryalei and others between May and September to prepare for a terrorist attack. Allnutt said the charge stemmed from the interception of a phone call a couple of days ago.

The latest raids followed the arrests of two people last week in Brisbane who were charged with allegedly recruiting, funding and sending self-declared jihadist fighters to Syria.

And, on Wednesday, a Sydney-based money transfer business was shut down amid concerns it was being used to funnel funds to the Middle East to finance "terrorism."