Turnbull announced on Sunday that "a terrorist plot to bring down an airplane" had been disrupted, but revealed few details.
Officials did not specify if the alleged plot targeted a domestic or global flight, but Sydney's Daily Telegraph reported that a local route had been the objective.
'This recognises that terrorism investigations are inherently complex and that there can be legitimate reasons for extended periods of detention for suspects in such matters, ' the AFP statement said.
"The office of transport security has advised security screening will take longer, and travellers should arrive at terminals at least two hours before flights to allow ample time for screening".
Security has been increased at Sydney Airport since Thursday because of the plot and has since been increased in all major Australian global and domestic terminals.
Five homes across Sydney - in the inner-city suburb of Surry Hills and the south-western suburbs of Lakemba, Wiley Park and Punchbowl - were targeted by NSW and Australian Federal Police officers in the raids.
Deakin University security expert Greg Barton said the first plot to target aircraft in Australia, which is the highest aspiration of many extremists, was a "pretty big threshold moment".
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.
The terrorist threat in Australia remains at "probable" according to ASIO.
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It is understood the plan was to use wood scrapings and explosive material inside a piece of kitchen equipment, such as a mincing machine.
Addressing media this morning, Prime Minister Malcolm Turnbull said that "the threat of terrorism is very real" and that security measures have been "enhanced and intensified". Five plots have been executed.
Police said there was no indication the integrity of airport security had been compromised.
Australian Federal Police Commissioner Andrew Colvin said terrorists were becoming "ingenious" about coming up with ways to bypass security, but he described the measures at Australian airports as some of the best in the world.
The arrests came almost two months after the deaths of two men in Melbourne in what police have called an act of terrorism.
The four, reportedly all family members, are accused of plotting to bring down a plane bound for the Middle East with an Islamic State inspired home-made bomb.
"I love Australia", she said as she was accompanied to a waiting vehicle by police.
"The reality with terrorism, ".
"You do have to go early because if you get it wrong, the consequences are severe".
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