Former US President Donald Trump, rapper Ye (formerly Kanye West), and influencer Andrew Tate accounts were all reactivated over the weekend.
Mr Musk responded to tweets in which many asked if Jones would 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
Among those calling for his release was controversial internet tycoon Kim Dotcom.
Jones stated in a video released on the platform Rumble that he does not care about being on Twitter, according to the 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 habitual tweeter until he was banned in January 2021 for allegedly inciting violence on the platform during the Capitol Hill protests.
In October 2022, Ye was banned for making an anti-Semitic post.
Andrew Tate was banned from many platforms for posting misogynistic remarks, such as implying that women should be held accountable 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.
(BBC)
