Apple was "extremely sorry" for the frustration experienced by customers using the new mapping program that had glitches and inaccuracies, he said, suggesting they investigate other mapping applications available in Apple's App Store or even seek solutions on the Web from competitors Google and Nokia.
Apple has called Maps a work in progress and Cook said the company was listening to user complaints.
"Everything we do at Apple is aimed at making our products the best in the world," Cook wrote. "We know that you expect that from us and we will keep working non-stop until Maps lives up to the same incredibly high standard."
Apple users have used the Map app to search for 500 million locations since its debut as part iOS 6 two weeks ago, Cook said.
A public apology is unusual for Apple and is a departure from its responses to problems in the past, The Washington Post said.