Former President Donald J. Trump declared on Wednesday evening that he would start a “media powerhouse.” Its flagship operation would be Truth Social, a Twitter-like social network that would “stand up to the tyranny of Big Tech,” he said in a statement.

Within two hours, hackers had gained access to a private version of the social network, creating fake accounts for Mr. Trump; the far-right personality Stephen K. Bannon; Ron Watkins, the QAnon conspiracy theorist; and Twitter’s chief executive, Jack Dorsey, who barred Mr. Trump from Twitter after his supporters stormed the Capitol on Jan. 6.

Using a false “donaldjtrump” account, hackers posted images of defecating pigs, wrote expletive-laced rants aimed at Mr. Dorsey and inquired about the whereabouts of the former first lady Melania Trump. Images of the hackers’ handiwork were circulated on other social media platforms.

In interviews on Thursday, the hackers, who are affiliated with Anonymous, the loose hacking collective, said the effort was part of their “online war against hate.”