Mr Musk, who took over the social-media platform in October, said it was "important to free up abandoned handles".
The move has been criticised online, as people feared losing access to accounts of relatives who had died.
But Mr Musk hinted this may be avoided, as old accounts would be archived rather than deleted.
One person asked about accounts of celebrities prominent on Twitter before they died, including chef Anthony Bourdain.
Another mentioned tweets that may hold historical value, such as those from victims of tragedies.