How can I restrict the "Send Message" feature?

Is there a way to restrict the “Send Message” feature like there is for the “Chat” feature?

I would like a registered user to have to create a profile before they get use of the “Send Message” feature. The way it is now all someone has to do is register and they have access to send messages using the link on other profiles.

Or is there a way to prevent registered users access to other profiles unless they have a profile themselves?