Thousands of Christians fled the northern Iraqi town of Mosul after IS gave the ultimatum: embrace Islam, pay tribute or face execution, on July 17.
Christians living in Baghdad are also living in fear amidst reports the IS have established hidden cells in the area.
"France and Kurdistan have been very generous in offering asylum to persecuted Christians," ACL Managing Director, Lyle Shelton, said.
"Australia should also share some of the burden."
While acknowledging that Australia has been engaged in assisting other world crisis, such as the war in Gaza, Shelton urged nation leaders not to overlook the needs of the minorities in northern Iraq, as well as in Syria.
"Christians have lived in this region for 2000 years and are the indigenous people of the area yet they are being driven out of their homes by murderous terrorists," he said.
On Monday, France offered to provide asylum to those forced to flee Iraq.
"We are ready, if they so desire, to help facilitate asylum on our territory," the Foreign and Interior ministers, Laurent Fabius and Bernard Cazeneuve, said in a statement.
An ACL petition calling on the Australian government to raise its humanitarian migrant intake can be viewed at www.makeastand.org.au.
