Justices Flavio Dino, Cristiano Zanin, Carmen Lucia and Luiz Fux sided with Moraes, with some of them saying however that the suspension could be reversed if the platform complies with previous court rulings.
X was taken down in Brazil, one of its largest markets, in the early hours of Saturday following a decision by Moraes, after the platform missed a court-imposed deadline to name a legal representative in Brazil as required by local law.
Moraes also ordered that those who continued to access X via VPNs be fined up to 50,000 reais ($A13,000) per day.
Moraes and X owner Elon Musk have been locked in a months-long feud after the social media giant challenged legal orders to block accounts implicated in probes of alleged spreading of distorted news and hate in Brazil.
"It is not possible for a company to operate in the territory of a country and intend to impose its vision on which rules should be valid or applied," Justice Dino said as he sided with Moraes.
"A party that intentionally fails to comply with court decisions appears to consider itself above the rule of law. And so it can turn into an outlaw."
Zanin said non-compliance with Brazil Supreme Court decisions was "extremely serious," arguing that "no one can develop their activities in Brazil without observing the laws and the constitution".
Elon Musk-controlled satellite internet provider Starlink told Brazil's telecom regulator Anatel on Monday it will not comply with a court order to block X in the country until its local accounts are unfrozen.
Anatel confirmed the information to Reuters on Monday after its head Carlos Baigorri told Globo TV it had received a note from Starlink, which has more than 200,000 customers in Brazil, and passed it onto Brazil's top court.
The shutdown of X also led to the freezing of Starlink's bank accounts in Brazil.
Starlink is a unit of Musk-led rocket company SpaceX.
Musk responded to the account block by calling Moraes a "dictator".
The decision to freeze Starlink's accounts stems from a separate dispute over unpaid fines X was ordered to pay due to its failure to turn over some documents.
