I don't know for sure, but I was told that if you hit *61, this will stop the calls. I haven't had a chance to try it yet, but I plan to.
I just checked it out and here is what I found on AT&T site:
I can understand the importance of blocking unwanted calls. I had some random telemarketer get a hold of my number and being able to block it, saved my sanity. I would be happy to help.
After researching more into the *61 code I'm showing it is for Digital Home phones. Just to verify it was a home phone only feature I tried it on a couple AT&T cell phones and received the same recording as you.
If you are interested in blocking suspected spam calls we have a great app called Call Protect. This is only compatible with certain phones, you can find more information including on how to download it here.
If there is a specific number you would like to block many phones offer call blocking on the device. Start on our great Device Support page, make sure your device is selected then choose Tutorials > Call > Block or Unblock Calls.
I hope this information helps and please have a splendid rest of your week!