The black Shahada flag - identical to those used by Islamic State - was sold by Markaz Imam Ahmad mosque in the western Sydney suburb of Liverpool for more than $2000 in July.
In a statement, the mosque denied it was supporting terrorism by auctioning the black and white flag, which it says is an "important symbol in Islam".
The mosque also insists the money raised from the sale of the flag was purely for the mosque and not to fund Islamic State in Syria or Iraq.
"This does not belong to them, it belongs to all of us."
However, the auction of the flag has sparked anger at both a state and federal government level.
Prime Minister Tony Abbott has warned that anyone working with groups listed as terrorist organisations will face investigation.
"It is a serious offence under Australian law to work with terrorist organisations, to fund terrorist organisations, to fight with terrorist organisations," Mr Abbott says.
"These are serious offences under Australian law and where there is evidence that Australian law has been broken it will be dealt with severely."
New South Wales Premier Mike Baird says his government is considering banning the flag.
"It is a flag that is used by ISIS and ultimately that we have to respond to and have a zero tolerance to," he says.
"We obviously understand and appreciate and are very mindful of the tradition of Islam and this in no way goes in any way shape or form against that. This is about a terrorist organisation and you can see what they are doing across the world, and it is horrendous. And so in this country we have to have a zero tolerance approach to anything that shows support for that."
However a community leader, Dr Jamal Rifi, says the mosque had no intention of supporting Islamic State.
"Probably this flag should not have been put for an auction," says Dr Rifi, who is the founding member of the Christian Muslim Friendship Society.
"But the people made this a couple of months ago, well before the atrocities of the barbaric state. It was a gesture mainly to raise some funds for the Markaz Imam Ahmad mosque in Liverpool."
"In no way did they want to show any support for the barbaric state and in no way was it endorsing their atrocities."
Dr Rifi says the flag has significance to all Muslims, and does not belong exclusively to Islamic State.
"It is a flag that all Muslims aspire to because it is the first flag that flew with the name that there is no God but God, and the Prophet is the messenger of God."
"It is a generic term. It is Shahada, which is the first pillar of all Muslims and it's been hijacked by the Islamic State the same way the cross has been hijacked by the Ku Klux Klan and we should look at it in its entirety."
"This does not belong to them, it belongs to all of us."
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