The app was developed by Facebook's photos team without the assistance of Instagram, because Facebook's $1.1bn acquisition of the photo-sharing service has not yet closed.
In a blog post, Facebook's Dirk Stoop said that the new Camera app "makes using Facebook photos faster and easier".
"When you launch the app, you'll see a feed of just great photos from the people you care about," he said. "You can swipe to see more of any album or tap to enlarge an individual photo."
Users can also edit their photos with new tools for cropping, rotating and adding 14 Instagram-like filters to any pictures of the camera roll.
While Camera is not quite as clean or beautiful as Instagram, a strong differentiation point is multi-photo uploads, which is useful for people wanting to share multiple photos from a day out or an activity.
"Now you can quickly share multiple photos all at once instead of having to post one at a time," said Stoop.
"Just select the shots you want to share by tapping the check-mark on each photo and then hit post. You'll have a chance to add a caption, say where you were and tag friends before you share."
Camera is available now for the iPhone from the Apple App Store. Facebook has not yet indicated whether it is working on versions for other phone platforms, such as Android, BlackBerry and Windows Phone.
The app is part of Facebook's strategy to better exploit the growing use of its service on mobile devices, following criticism that Mark Zuckerberg's firm has been slow to the mark.
Even after the Instagram acquisition is completed, Facebook has pledged to keep the photo app going as an independent business, and so it is anticipating some "healthy competition" with Camera.
A Facebook spokesman told TechCrunch: "We're committed to building and growing Instagram independently, so I anticipate some healthy competition."
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