This week,Parliament's bipartisan human rights committeefound changes to the act would not contravene Australia's international obligations.
Family First senator Bob Day has now proposed removing the words"insult"and"offend"from the act,meaning it would no longer be a prosecutable offence to insult or offend someone based on their race.
Liberal senators Cory Bernardi and Dean Smith have previously pledged their support and have co-sponsored Senator Day's bill. It is also being co-sponsored by Liberal Democrat senator David Leyonhjelm.
Supporters for the change renewed their push in the wake of theCharlie Hebdoterrorist attack,in defiance of Mr Abbott's decision.