The maximum penalty for each offense is life in prison.
Turnbull said the plot involved bringing down a passenger plane. AFP Commissioner Andrew Colvin said the plan had been to use an "improved device."
No further official details have been released.
The AFP would not confirm or deny the report and Minister of Immigration Peter Dutton told media he didn't "want to go into the detail."
Multiple raids following arrests
Multiple raids have been carried out at multiple properties across Sydney by law enforcement authorities since Saturday, including the suburbs of Surry Hills, Lakemba, Wiley Park and Punchbowl.
Earlier Thursday, Turnbull said the threat to aviation in Australia had been "disrupted and contained" following the arrests and the level of security at airports was being lowered.
Stricter airport security measures had been put in place following the attack, with Australian airports warning of possible delays and longer check-in times.
At the same press conference, Turnbull said a "very substantial" amount of evidence had been uncovered and investigations were ongoing.
The two men facing charges will appears in a Sydney court on Friday morning.