Australian police on Thursday made a series of arrests in pre-dawn counter-terrorism raids across Sydney and Brisbane, with those detained reportedly suspected of links to the jihadist group Islamic State.

The operation, which spanned numerous suburbs, comes barely a week after the country raised its terror threat level to "high" for the first time in a decade on growing concern about militants returning from fighting in Iraq and Syria.

Police said the raids were ongoing and hundreds of officers were involved. They did not say how many arrests were made, but the Australian Broadcasting Corporation said at least a dozen people were taken for questioning.

They followed the arrests of two people last week in Brisbane who were charged with allegedly recruiting, funding and sending 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.

The latest raids came after months of surveillance of people believed linked to the Islamic State group of extremists, local reports said.

The government believes up to 60 Australians are fighting alongside jihadists for Islamic State, while another 100 were actively working to support the movement at home.

Last week's decision to raise the terror threat level after years on "medium" officially means a "terrorist attack is likely", and comes after repeated government warnings that attacks could happen.

The lifting of the threat level was "not based on knowledge of a specific attack plan but rather a body of evidence that points to the increased likelihood of a terrorist attack in Australia", Prime Minister Tony Abbott said at the time.

"Security and intelligence agencies are concerned about the increasing number of Australians working with, connected to, or inspired by terrorist groups such as ISIL (Islamic State), Jabhat Al-Nusrah, and Al-Qaeda," he said.

"The threat they pose has been increasing for more than a year."

The "high" alert is just below "extreme" -- the top level -- which would indicate a "terrorist attack is imminent or has occurred".