Set up role for self registration
1. In the admin panel, go to Users -> Roles and create new role, for example "Commentors".
2. Assign to this role same rights that "Anonymous" role has.
Revoke "Create comment" right from anonymous
In the "Roles" screen, click anonymous role and uncheck "Create Comment"..
Set up self registration
1. In the admin panel, go to Settings -> Advanced and under "Security Settings" section check "Enable self
registration". This will add registration option to logon screen.
2. In the "Initial Role" dropdown, select "Commentors" role created in the first step.
With this in place, only logged in users should be able to post comments.