Department head said that group project may be rejected. How to mitigate?
It seems like this will come down to your university's rules and the personalities involved. Still, let's consider:


  He mentioned by email that university norms require 4 people working on a group project and the Academic Registrar's permission would be required to do it alone. 


So you were very specifically told, in writing, that you would need to get approval from the registrar.


  I replied (cc'ing my mentor) asking if I would have to meet the registrar. I received no reply. 


And you didn't get approval from the registrar. As a "working professional", you should know that you can't just send one e-mail and then drop the matter -- it's your responsibility to run this to ground. 


  My mentor asked if I got the Registrar's permission.


Well that was predictable


  During the entire two months my mentor, the HoD and even classmates were aware that I was doing the project alone.


They probably assumed that you had gotten approval from the registrar as they had told you to. It would have been nice if they had followed up on this, but this is not their responsibility.


  I'm a working professional. Working in groups is an everyday job. Even companies have realized that certain people perform better when not in a group and are hired as "individual contributors". What is a university's purpose in forcing people to work together.


This is very much not the point. The program can impose whatever (reasonable) requirements it wants. Learning to work in groups is a reasonable goal, regardless of whether you personally already have background working in groups.


  What would be the right way to respond to him without sounding defensive?


This is the part that comes down to your university's rules and the personalities involved. It may be that this is a strict rule and there is nothing that anyone can do. Or, it may be that there is a process for an appeal or exception. I would start by recognizing that you are in the wrong.