The chief of the Australian Defence Force, Air Chief Marshal Mark Binskin, made the announcement via Twitter on Monday morning.

Two F/A-18F Super Hornets conducted the flights but did not fire any weapons, he said.

In a statement, the ADF said the two planes were "on-call to attack targets as identified".

"On this occasion, the aircrat did not use their munitions and have returned to base to disarm and prepare for future sorties," the statement read.

The Super Hornets were supported by an Australian Air task Group KC-30A, while an E-7A Wedgetail Airborne Early Warning and Control aircraft also flew over Iraq overnight.

The flights were completed "without incident and all aircraft have reurned safely" to Australia's main support base in the Middle East.

The government's National Security Committee gave the nod to air combat operations on Friday. The full cabinet then approved the action and the opposition was also briefed.

As well as 400 RAAF personnel, the Abbott government has deployed 200 special forces commandos to the Middle East where they are awaiting final orders to enter Iraq and begin an "advise and assist" role with local forces.

2 F/A-18F completed 1st armed combat mission in Iraq. No munitions expended. Returned safely to base. — Mark Binskin (@MarkBinskin_CDF) October 5, 2014

Fairfax Media understands that the focus of the special forces' role on the ground in Iraq will be to build up the confidence and discipline of the junior and mid-ranking officers, many of whom fled from major battles in recent months, causing their troops to scatter.

Defence Minister David Johnston yesterday rejected suggestions that Iraqi ground forces were inadequate to the task of driving the Islamic State out of towns and cities.

While acknowledging the Iraqi army was "a little bit disjointed" and had been "allowed to run down", Senator Johnston said there were "pockets of … highly professional and highly capable Iraqi security forces".

He indicated on the ABC's Insiders program that he viewed the ground war as being a "counterinsurgency" - the firmest acknowledgement yet that it could involve a difficult and drawn-out fight marked by guerrilla-style tactics in urban areas.

"The counterinsurgency service of the Iraqi security forces is very capable and very good and we'll be working with them more than likely," he said. "We are optimistic that we can put them up in a position where they can resecure many of these towns."

It is understood this could mean the Australian special forces work with Iraq's elite Special Operations Forces - the counter-terrorism commando brigade set up by the Western coalition in the wake of the 2003 overthrow of Saddam Hussein.

More to come