iTunes Account Creation not allowed

Is it possible to solve "iTunes account creation not allowed" problem?

I have just created a new Apple ID, added redeem code from Apple gift card and tried to download the app from App Store. After tapping [Get], entering Apple ID Password, I see "Done", but then the ring starts spinning for a sec and the error is displayed.

I tried rebooting the device, signing in and out of the App Store and Apple ID, no sandbox is used. Checked on several devices, however, the problem remains. I guess something is wrong with the Apple ID. Can you please help?