mysql server secure installation script always fail with error while entering root password.

Issue

• On a new install of mysql-server package, mysql server secure installation script /usr/bin/mysql_secure_installation always fail with following error when entering the current root password.

Enter current password for root (enter for none): 
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

Eg:

[root@example ~]# /usr/bin/mysql_secure_installation

NOTE: RUNNING ALL PARTS OF THIS SCRIPT IS RECOMMENDED FOR ALL MySQL
      SERVERS IN PRODUCTION USE!  PLEASE READ EACH STEP CAREFULLY!

In order to log into MySQL to secure it, we'll need the current
password for the root user.  If you've just installed MySQL, and
you haven't set the root password yet, the password will be blank,
so you should just press enter here.

Enter current password for root (enter for none): 
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)