The improvised explosive device was intended to be smuggled on to a flight on 15 July but the plan was aborted before it reached airport security.
Australian Federal Police Deputy Commissioner Michael Phelan said the instructions to the group were “coming from a senior member of the Islamic State”.
Mr Phelan described this person as a “commander” based overseas.
Police said the commander had organised for the parts of the IED to be sent to the men in Australia via international cargo from Turkey and that he had instructed them on how to build the bomb.
“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.”
Mr Phelan described the explosive as “high-end”, adding: “I don’t want to be specific because it’s still under examination for the exactness of it but high military-grade explosive”.
“This is one of the most sophisticated plots that has ever been attempted on Australian soil.”
One of the men had brought the device to Sydney airport in a piece of luggage he asked his brother to take with him on the flight, Mr Phelan said, adding that the brother had not been told about the bag’s contents.
But, for some reason, the man had left the airport with the bag and the brother, who has not been charged in relation to the plot, continued onto the flight without it.
“There is a little bit of conjecture as to why it didn’t go ahead. It didn’t get past the check-in,” he said.
A second plot, hatched after the failure of the first, is alleged to have involved a “chemical dispersion device” which would release highly-toxic gas, described as having been in the early stages.
No target had been chosen but an Islamic State member had given the men suggestions, such as crowded areas or public transport.
Mr Phelan said the hydrogen sulphide gas was “very difficult to make”, adding that “while it may be a hypothetical plot, we were a long way from having a functional device”.
He said: “Not only have we stopped the IED that was believed to go on the plane but we have also completely disrupted the intended chemical dispersion device.”
Khaled Khayat, 49, and Mahmoud Khayat, 32, have been charged with two counts of planning a terrorist act.
Barrister Michael Coroneos appeared on behalf of both men at a brief court hearing on Friday in Sydney, and the case was adjourned until 14 November.
Outside court, Mr Coroneos said they were “entitled to the presumption of innocence” and declined to answer any other questions.
Police allege the men began communicating with Islamic State in April. They were arrested on 29 July, three days after Australian authorities received a tip from intelligence agencies.
A third man is still being questioned and a fourth was released without charge.