The app was launched with iOS 6 on Wednesday but users have complained that it is not a patch on the Google Maps app it replaces.
The app, downloaders say, puts towns and cities in the wrong place, shrinks them or even sometimes just leaves them out altogether.
On one map of Sweden, for instance, Gothenburg, the country's second largest city, seems to have disappeared and, in Germany, Berlin's main station, Hauptbahnhof - renamed six years ago - has revered to its former name of Lehrter Stadhbahnhof.
One irritated customer has set up a tumblr to show exactly what is wrong.
Now, Apple says it is going to put things right.
In a statement to AllThingsD , a website specialising in news, analysis and technology, the company said: "We launched this new map service knowing it is a major initiative and that we are just getting started with it.
"Maps is a cloud-based solution and the more people use it, the better it will get. We appreciate all of the customer feedback and are working hard to make the customer experience even better."
The online blog from John Paczkowski says Apple developers working on the fixes are "in lockdown" until they come up with a solution.
Apple's app is based on TomTom's map data.
TomTom insists there is nothing wrong with its information and said each manufacturer makes their own unique application under license.