"The mission was conducted by a RAAF C-130J Hercules delivering 10 pallets of badly needed supplies to Yazidi civilians trapped on Mount Sinjar by encircling ISIL forces," he said, referring to Islamic State militants, previously known as ISIL.
The cargo included 150 boxes of high energy biscuits and 340 boxes of bottled water - enough to sustain 3,700 people for 24 hours.
"Initial reports are that the drop was conducted successfully and the aircraft is returning to base," Abbott added.
The United Nations has said tens of thousands of members of minority groups, including Yazidis and Christians, were stranded on Mount Sinjar and facing "a mass atrocity and potential genocide within days or hours".
However, the Pentagon said yesterday that - based on a firsthand assessment by a small party of US troops - the plight of those stranded was better than feared, and an evacuation mission "is far less likely".
The US yesterday conducted its seventh airdrop of food and water, while British Prime Minister David Cameron said an international plan was under way to rescue those trapped.