Justice Moraes gave X 24 hours to name a new legal representative or face suspension, with the deadline coming just after 20:00 local time (23:00 GMT) on Thursday.
The order said a ban would remain in effect until X names a legal representative in the country and pays fines for alleged violations of Brazilian law.
But in a post from one of its official accounts shortly after the deadline expired, X made clear that it had not complied with the order.
“Soon, we expect Judge Alexandre de Moraes will order X to be shut down in Brazil – simply because we would not comply with his illegal orders to censor his political opponents,” the post said.
“The fundamental issue at stake here is that Judge de Moraes demands we break Brazil’s own laws. We simply won’t do that.”
X said it would not comply “in secret with illegal orders”, adding that it would publish the judge’s demands in the coming days “in the interests of transparency”.
Justice Moraes had ordered that X accounts accused of spreading disinformation – many supporters of the former right-wing president Jair Bolsonaro – must be blocked while they are under investigation. He said the company’s legal representatives would be held liable if any accounts were reactivated.
Meanwhile, the bank accounts of Mr Musk’s satellite internet firm Starlink have been frozen in Brazil following an order by the country’s Supreme Court.
Starlink responded with a post on X which said the “order is based on an unfounded determination that Starlink should be responsible for the fines levied – unconstitutionally – against X.”
Mr Musk also said on X that “SpaceX and X are two completely different companies with different shareholders.”
Starlink is a subsidiary of Mr Musk’s rocket firm SpaceX.
In 2022, the government of then-President Bolsonaro gave Starlink the green light to operate in Brazil.
As South America’s largest country, Brazil and its remote regions in the Amazon have huge potential for Starlink, which specialises in providing internet services to isolated areas.
Justice Moraes gained prominence after his decisions to restrict social media platforms in the country.
He is also investigating Mr Bolsonaro and his supporters for their roles in an alleged attempted coup on 8 January last year.
X is not the first social media company to come under pressure from authorities in Brazil.
Last year, Telegram was temporarily banned over its failure to cooperate with requests to block certain profiles.
Meta’s messaging service Whatsapp also faced temporary bans in 2015 and 2016 for refusing to comply with police requests for user data.
