The platform's Global Government Affairs team on Saturday said Australia's eSafety Commissioner had ordered it to remove some posts that commented on the attack.
But it said the posts did not violate X's rules on violent speech.
The platform claimed the Australian regulator had demanded X "globally withhold these posts or face a daily fine of $785,000".
"X believes that eSafety's order was not within the scope of Australian law and we complied with the directive pending a legal challenge," the Global Government Affairs account posted on Saturday.
"While X respects the right of a country to enforce its laws within its jurisdiction, 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."
The recent attacks in Australia are a horrific assault on free society. Our condolences go out to those who have been affected, and we stand with the Australian people in calling for those responsible to be brought to justice. — Global Government Affairs (@GlobalAffairs) Following these events, the Australian eSafety…April 19, 2024
The commissioner has only said it was considering whether further regulatory action was warranted, after it put social media platforms on notice to remove graphic content showing recent violence in Sydney.
Federal Health Minister Mark Butler said the government would take X to task if it wanted to pursue the matter in court.
"Australia is not going to be bullied by Elon Musk, or any other tech billionaire, in our commitment to making sure that social media is a safe space," Mr Butler told reporters in Adelaide.
"So if he wants to fight that fine in court, well, we're up for that fight."
Calls have grown for harsher sanctions for social media platforms in the wake of the April 13 shopping centre massacre at Bondi after distressing footage of the attack was uploaded online and misinformation spread.
NSW Premier Chris Minns said X had shown "disregard for the information that they pump into our communities".
"Then when things go wrong, throwing their hands up in the air to say that they're not prepared to do anything about it," he told reporters.
Bishop Mar Mari Emmanuel was allegedly stabbed during a church sermon. (HANDOUT/Christ of Good Shepherd Church)
The premier and other leaders met with Assyrian community groups after the church stabbing and they collectively condemned violence.
"If anyone acts in that way, they are doing it in complete defiance of the religious leadership of NSW and it is against the law," Mr Minns said.
A 16-year-old boy was charged with terrorism offences over the church stabbing and is next due to face court in June.
On Friday evening, 45-year-old Sam Haddad was arrested at a Fairfield Heights home and charged with rioting and threatening violence, causing fear.
Haddad fronted Parramatta Bail Court on Saturday and was granted bail on the condition he report to police every day and live at a specific address.
He is next due before Fairfield Local Court on Wednesday.
A 28-year-old man was also charged over the incident and was due to face court on Saturday.
Police hope high-visibility patrols in the region will curb conflict after the knife-wielding teenager allegedly struck Bishop Mar Mari Emmanuel, 53, who was delivering a sermon on Monday night.
The stabbing triggered a riot outside the Christ the Good Shepherd Church in Wakeley. (Bianca De Marchi/AAP PHOTOS)
The stabbing - which has since been declared an act of terrorism - triggered a riot outside the Christ the Good Shepherd Church in Wakeley, leaving dozens of police officers injured.
The lawyer of the boy charged over the stabbing told a court the teenager had received intermittent treatment for his mental health for years.
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