"So now I have two apps on my phone to do the work of the one old app? Wonderful. I'd like to leave zero stars but it won't let me," one reviewer wrote on the Apples App Store review page.
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Another reviewer also raised privacy concerns, claiming the app would "take control of your phone, use your data, call and text using your phone without you knowing, take pics without you knowing, use yours and all your contacts personal info, etc. Basically you sign your rights away."
Facebook did not respond to CNBC's request for comment, but said on an official website post that the app needs "certain permissions" to work, such as allowing access to the camera in order for a user to take pictures.
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Facebook Messenger is part of the social network's multi-app strategy as it looks to gain dominance on smartphones. Mobile advertising revenues represented nearly two thirds of the company's $2.68 billion total advertising revenues in the second quarter of 2014 showing the importance to its top line.
The average American spends 40 minutes a day checking their Facebook feed, the company said earlier this year, underlining how the company could use its flagship app to send people to other apps in its network.
Facebook has indicated that it will release a number of standalone apps this year and began with a newsreader app called Paper in January. It also releasedSlingshot as a challenger to Snapchat, an app that allows users to send videos and pictures that disappear when viewed.