Two of those men appeared in a Sydney court on Friday charged with "preparing for, or planning, a terrorist attack".
The maximum penalty for this charge is life imprisonment.
Prime Minister Malcolm Turnbull described the plot as "major" and "elaborate".
Little has been confirmed officially but authorities have said the plot involved plans to "bring down" an aircraft using an "improvised device".
A fourth man, 50-year-old Abdul Merhi, was released without charge on Sunday night.
A domestic meat mincer turn into a home-made explosive, which could explode or leak poisonous gas, was a suspected weapon. He told reporters in Perth that the times passengers had been advised to arrive at airports would return to normal after being extended in response to the alleged plot which "has been disrupted and it has been contained".
However, Mr Phelan said that plan was not close to being realised when police conducted raids on Saturday and arrested four men.
Increased airport security measures introduced after the arrests have caused delays for some air transport operators.
"The Etihad Airways aviation security team is assisting the Australian Federal Police with its investigation and the matter is ongoing", it said.
Merhi's lawyer Moustafa Kheir said his client had endured intense questioning.
"Etihad is complying fully with the enhanced security measures at airports in Australia and monitoring the situation closely", it said.
"With assistance from the ISIL commander, the accused assembled the IED into what we believe was a functioning IED to be placed on that flight", said Phelan.
The attack was allegedly planned to be carried out aboard an airplane using an improvised device, one that was likely created to be hidden inside a "meat grinder", according to the U.S. State Department.
Mr Turnbull announced the threat level for Australian aviation had been downgraded to "possible" on advice from the head of Australia's spy agency ASIO.
Australian law gives investigators seven days to interrogate those in custody and uncover the plot.
The discovery was only made after the arrests of the men on the weekend.
Sources told Fairfax they believe the device might have been detected during security screening had it got any further.