We had reported earlier that Instagram is supposed to introduce private messaging to their Android app. On 12th December 2013 Instagram introduced a version of private messaging which allows users to send photos to only one or a few of their followers at a time.
Communication between Instagram users to date has been limited mainly to proxy networks. Now, it increases the continuing battle with Twitter. We presume that Twitter is working on something.
Kevin Systrom (Founder of Instagram) said in an interview;
Source : All ThingsD