In a letter published on Friday on Apple’s website, Tim Cook said the firm “fell short” on the product, and was “extremely sorry”.
“At Apple, we strive to make world-class products that deliver the best experience possible to our customers,” he wrote.
Mr Cook took the unprecedented step of advising users that other products were available.
“While weĆ¢??re improving Maps, you can try alternatives by downloading map apps from the App Store like Bing, MapQuest and Waze, or use Google or Nokia maps by going to their websites and creating an icon on your home screen to their web app.”
Apple launched the maps service earlier this month after dumping Google’s maps in the latest version of its iPhone and iPad software.
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Instead, it decided to create its own, using partners such as TomTom for data, while also using helicopters and planes to create 3D maps of major cities.
This led to outrage among users who flooded Twitter and Facebook with examples of Apple’s flawed maps.
Errors noticed by users and tech reviewers included major towns such as Stratford-upon-Avon appearing to be missing, searches for Manchester United Football Club bringing up Sale United – a football club for the over-fives, and large parts of the world obscured by cloud in satellite views.
The Apple service is server-based, the firm said, so the data is constantly being refined and improved.
Users are also encouraged to use a ‘Report a Problem’ feature to point out errors.