Facebook API login error on private script. How to fix it?

I am searching everywhere, but I can't find the right solution for my problem. I am trying to create a web service which requires Facebook API login.

When I try to log in with my account (admin) I get this message:

App Not Setup: This app is still in development mode, and you don't have access to it. Switch to a registered test user or ask an app admin for permissions.

Most people get this error when they forget to make their app public, but my APP is already public (Your app is currently live and available to the public.) and has a valid email address.

Any ideas what could be wrong? Thank you.