“They are outright banning people, and they are blocking conservatives involved in their own First Amendment political speech,” he said.
Mr. Jones also broadcast video on Periscope of himself on Wednesday insulting the CNN reporter Oliver Darcy. Mr. Darcy had previously reported on tweets by Mr. Jones that appeared to violate Twitter’s policies.
The video of Mr. Jones’s harassing behavior toward Mr. Darcy was among the material that Twitter considered before deciding on the bans, according to a person briefed on the situation, who was not authorized to speak publicly.
In his Periscope broadcast on Thursday, Mr. Jones defended his behavior toward Mr. Darcy, saying the CNN reporter is a public figure and had bullied tech companies into barring Mr. Jones. He suggested, without evidence, that Twitter had barred him to protect CNN and Mr. Darcy because the news organization was part of a government conspiracy.
“CNN is part of this C.I.A. stay-behind network that I brought up, that Obama set up, that we’re telling the president about,” Mr. Jones said.
Mr. Darcy referred requests for comment to a CNN spokeswoman, who declined to comment.
Twitter said it had followed routine procedures in permanently suspending the accounts of Mr. Jones and Infowars. The company typically issues temporary suspensions, like the one Mr. Jones received last month, before enacting a ban.
Mr. Jones is one of the most prominent alt-right figures to be barred from Twitter. In 2016, the company barred Milo Yiannopoulos, a former editor of Breitbart, for his involvement in an online harassment campaign against the actress Leslie Jones. Another former Breitbart writer, Chuck Johnson, was suspended for threats toward the civil rights activist DeRay Mckesson. Twitter also bars hate groups like the American Nazi Party and Golden Dawn, an ultranationalist organization based in Greece.
In a final tweet before his Twitter account vanished, Mr. Jones posted a photo of himself sitting behind Mr. Dorsey during Wednesday’s congressional hearings. On the photo was the hashtag #FreeAlexJones.