Android 5.1.1 - cannot add Google account; getting stuck on "add phone number?"

I am now trying to get my old phone to life. This is Nexus 4 with Android 5.1.1. I have successfully restored it to the factory, now I am trying to configure it with my Google account. Unfortunately, each time I enter a password, it redirects me to the "Add phone number?" screen and I get stuck there - links "more info", "skip", and "I'm in" simply do not work. The only thing I can do is cancel the whole operation. I also gave a try with another Google account - it also got stuck on the screen asking "Who will be using this device?". Is there any way to configure the account?