Mozilla already offers Firefox on Android, but the OS makes up just a sliver of total Web traffic on mobile, easily surpassed by Google's Chrome browser and Apple's Safari, according to data from StatCounter.
Overall usage of Firefox across desktop and mobile has fallen in recent years, according to Web analytics company W3Counter.
Creating a version of Firefox for iOS has required Mozilla to retool its back end because Apple's App Store only allows browsers that are built atop Apple's rendering and JavaScript engines.
But Mozilla appears to be making progress. On Thursday, the company said it was rolling out the first public preview version of the browser for iOS in New Zealand. It plans to extend availability to a few more countries soon.
Feedback from the preview release will help Mozilla build new features and launch Firefox for iOS in the rest of the world later this year, the company said in a blog post on Thursday.
For the iOS release, one of the features Mozilla is testing is Firefox Accounts. It will let users take their Firefox browser history, passwords and tabs from the desktop to iOS devices.