Can't connect using host name

[Chakravarthy Cuddapah]

MySQL ver 5 has been installed on Mac OS X Server 10.6.8.
I can connect from the terminal on the same system using:
mysql -u root -p which works without any issues. But when I try using host name or IP address as below I get an error message:
mysql -h host_name -u user_id -p
or
mysql -h ip_address -u user_id -p
Error message is :
ERROR 2003 (HY000): Can't connect to MySQL server on 'host_name' (61)

I verified the user_id has full access for:
host_name, ip_address, %

I need this to work so the db can be accessed remotely. Appreciate any help.