Elon Musk says he will not allow the conspiracy theorist Alex Jones to return to Twitter.
Over the weekend the accounts of former US president Donald Trump, rapper Ye (formerly Kanye West) and influencer Andrew Tate were all reactivated.
Mr Musk responded to tweets asking if Jones could be next.
He wrote that his own child had died, and that he "had no mercy" for anyone who "would use the deaths of children for gain, politics or fame".
Nevada Alexander Musk died aged 10 days old in 2002.
Mr Musk said his baby died in his arms and he "felt his final heartbeat".
Info wars host Jones has been forced to pay $1.44bn (£1.2bn) in damages after falsely and repeatedly claiming that the Sandy Hook school shooting, in which 20 children and six adults were killed, was a hoax.
In August 2018 he was banned from Facebook, Spotify, Apple and YouTube.
Those asking for his return included the controversial internet tycoon Kim Dotcom.
On a video posted on the platform Rumble, Jones said he did not care about being on Twitter, reports news website Axios.
Mr Trump has yet to tweet, despite his reactivated account now having more than 90 million followers.
He has said he intends to stay on his own platform, Truth Social, although this has a fraction of the audience of Twitter.
Mr Trump was a prolific tweeter until he was banned for allegedly inciting violence on the platform during the Capitol Hill riots in January 2021.
Ye was banned for an antisemitic post in October 2022.
Andrew Tate was banned from several platforms for sharing misogynistic content, such as suggesting that women should bear responsibility for sexual assault.
Both Ye and Mr Tate are now tweeting.
Mr Musk had previously said no decision about banned accounts would be made until a moderation board had been appointed.
He completed his $44bn purchase of Twitter on 28 October after months of wrangling.
He has since laid off half of the firm's 7,500-strong workforce, and hundreds more staff are believed to have left following an email saying that long hours and "hardcore" work would be required of those who remained.
Mr Musk says that more people than ever are logging on to Twitter - but there is no official confirmation of this, as there is no longer a communications team.