Error while trying to clean install OS X El Capitan (Apple ID auth error)

I am trying to do a clean install of El Capitan using guide on support.apple.com. I reformatted they drive as told, but now I am getting an error while trying to do the new install. Every time I try to log in with my Apple ID, I get the following error:

AMD-Action:authenticate:SP

I have no clue why this is happening. I am doing a reinstall of macOS Sierra on my other mac and this is going as it should. I also see the device logged into the Apple ID when checking it on appleid.apple.com.

Does anyone know how I could get out of this? I don't have any backups, so I really need to do this install.

it's an Apple id problem. Solution: Power on your Mac and keep Command+Option+R (CMD+ALT+R) Then connect your wifi network and install without Apple id. i tested, it's work.