I have just come to Japan this month. I will be working for a company and be covered by Employees’ Pension Insurance system. Do I have to enroll in National Pension system for this month?

Yes. Persons must be covered by National Pension system as the Category I insured person for the period from the month of their entry to Japan to the month previous to enrolling in Employees’ Pension Insurance system.
You need to register yourself by submitting the “Application to Enroll in National Pension as Category I Insured Person” (KOKUMIN NENKIN HIHOKENSHA KANKEITODOKESHO (MOUSHIDESHO)) at the municipal office of your place of residence.
For more information about National Pension coverage, please visit: National Pension System (Coverage)