Bishop Mar Mari Emmanuel was allegedly slashed in the head and chest by a 16-year-old suspect on Monday, sparking a riot by followers of the Assyrian Christian church in western Sydney.
The bishop has since issued a message from hospital saying he is recovering from his wounds and has forgiven his assailant.
Video of the bloody attack, which spread widely on social media platforms, has been blamed by Australian authorities for feeding tensions in the community.
X's government affairs department said it had complied with an initial eSafety directive, "pending a legal challenge", to remove "certain posts in Australia that commented on the recent attack".
But the social media platform said it later received a demand from Australia's eSafety commissioner Julie Inman Grant to "globally withhold the posts".
X said it had been warned it faced a daily fine of Aus$785,000 (US$500,000) for failure to comply.
"The Australian censorship commissar is demanding *global* content bans!" Musk wrote as he reshared the company's response.
"The eSafety Commissioner does not have the authority to dictate what content X's users can see globally. We will robustly challenge this unlawful and dangerous approach in court," X said.
- 'Shocked' -
X said the posts did not violate its own rules on violent speech.
The eSafety watchdog said Friday it was working to ensure X's "full and complete compliance" with Australian law.
"We are considering whether further regulatory action is required," it said.
The authority said it was "disappointed that process has been unnecessarily prolonged rather than prioritising the safety of Australians and the Australian community".
eSafety said it was also working with major social media platforms over the reposting and sharing of content that shows or encourages terrorism or other extreme violence.
New South Wales Premier Chris Minns has been scathing of the role played by some platforms in making violent images of the attack available.
"I'm shocked but I'm not surprised," he said Saturday when asked about X's statement.
"That is exactly what I would expect from X or Twitter or whatever you want to call it: a disregard for the information that they have pumped into our communities, lies and rumors spreading like wildfire," Minns said.
"And when things go wrong, throwing their hands up in the air to say they're not prepared to do anything about it."
Minns called for a strengthening of the rules governing social media companies.
"We have had enough. Sydney has had enough."
