SYDNEY, Australia — The Australian police described on Friday an elaborate terrorist plot in which two men from Sydney tried to place an explosive supplied by the Islamic State on a flight last month, an operation that officials said was among “the most sophisticated plots that has ever been attempted on Australian soil.”

The two men, who have been charged with planning a terrorist act, were scheduled to appear in court via video link on Friday, and they were refused bail.

The Australian Federal Police said the charges covered an aborted attempt last month to place an explosive on an Etihad Airways flight from Sydney. The discovery of the plot led the authorities to tighten airport security around the nation last weekend.

As part of the plot, one of the men brought the explosive device to the Sydney airport in a piece of luggage, and asked his brother to take the luggage on the plane without disclosing its actual contents. But the bag never made it onto the flight for unknown reasons.

Officials said the discovery of the plot was the 13th significant threat that the police had exposed and broken up since Australia raised its terrorist threat level to probable in 2014.