Mr Turnbull said security had been increased at all major global and domestic airports around Australia.
Four men arrested in raids in Sydney late Saturday two Lebanese-Australian fathers and their sons had yet to be charged. They are being held under anti-terror legislation that gives investigators a week to bring charges, but requires a magistrate's periodic review and consent.
Security remains heightened in airports around Australia with more intense screening of luggage after law enforcement officials said they had thwarted a plan to bring down an airliner.
Australian prime minister Malcolm Turnball said the plot appeared to be "elaborate" rather than a lone wolf attempt.
The terror threat has caused fear among Australians, and an aviation security expert said Australia lacks the proper equipment for their security measures, reports News AU.
Security was increased at Sydney Airport from Thursday, but on Sunday this was extended to all major airports nationwide.
The foiled Australian terrorist plot targeting an airline, believed to be inspired by ISIS, has gotten the attention of the U.S. Department of Homeland Security. "Some of the measures will be obvious to the public, some will not be", Turnbull said.
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Passengers flying out of Newcastle Airport are being told to get there 30 minutes earlier than usual due to increased security measures.
While commuters at Sydney Airport and Adelaide Airport faced a chaotic scene of long queues as a result of the additional screening methods, Brisbane Airport was largely spared from delays or extra waiting times.
For passengers taking a domestic flight, they were advised to arrive at least two hours before their trip while those taking an worldwide flight may arrive three hours earlier.
Police previously said the men planned an attack on targets which included police headquarters in Sydney, along with civilian targets.
Turnbull would not speculate on how long airport security would remain elevated.
But a number of users on social media praised Qantas and Sydney airport workers for getting passengers through quickly. The offences are not related to the alleged plane bomb plot.
The plot was the 13th significant threat disrupted by police since Australia's terrorist threat level was elevated in 2014, Justice Minister Michael Keenan said.