Australian Mohammed Elomar sparked international condemnation when a photo of him brandishing two heads appeared on Twitter last week.
It prompted Mr Elomar to post news of the warrants on his Twitter account @Abuhafsashami.
He told one supporter that the Australian media is "a cancer" involved in a "war on islam".
Mr Elomar promised to continue operations as soon as he recovers from a knee injury.
BuzzFeed contacted Twitter about the account @Abuhafsashami and whether Australian authorities had asked for it to be shut down. Twitter subsequently suspended the account this morning.
On ABC's 7:30 program on Tuesday night, Australia's Attorney-General George Brandis spoke about the need to detain and investigate the Australian ISIS fighters who had been involved in recent conflicts in Iraq and Syria.