I am able to register and sync the contact using Audience Manager APIS in Tridion 2013 SP1. But I am not able to login via this user.
This can happen if the Address Book isn't set to be synchronized to the subscription database.
Make sure you add the Address Book to the "Audience Management" tab of a Publication which uses the right Synchronization Target. Also make sure that the "Synchronize Address Book" checkbox is checked (and thus the "Synchronized" list column says "Yes" next to the Address Book).