Apple chief executive Tim Cook apologized for the company’s new Maps application in a letter posted to the company’s Web site on Friday.

Cook said that Apple was “extremely sorry” for the frustration that customers have had with Maps and that the company is working hard to improve the application. He also pointed users to other mapping applications available in Apple’s App Store — from Bing, MapQuest and Waze — or through the Web from competitors Google and Nokia.

“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 had already been putting out the word through its press office that Maps was a work in progress and that the company was listening to user complaints.

But posting a public apology — from the company’s chief executive, no less — is a stark departure from past Apple actions.

The last time Apple acknowledged a problem with one of its products so publicly was when the company held a press conference on the antenna issues with the iPhone 4. At that event, while late Apple co-founder and CEO Steve Jobs agreed to issue a free bumper case to every iPhone 4 user, he also took pains to point out that the iPhone wasn’t alone in having those problems and that interference only happened when the phone was held a certain way.

He even famously told one customer who wrote asking about the issue that he/she should simply “avoid holding” the phone that particular way.

Cook also offered some hints about how the company split with Google on the search engine’s Maps application, which Apple rolled out with its updated operating system, at the same time eliminating Google Maps from iOS 6. He said that Apple wanted to provide an application it built from “the ground up” that had features including turn-by-turn directions, voice integration, Flyover and vector-based maps. Reports have surfaced that Apple and Google — being both business partners and fierce rivals — were having trouble coming to terms over some of those features when Apple decided to strike out on its own.

Maps users, Cook said, have already searched for half a billion locations since iOS 6’s debut two weeks ago.

Related stories:

Dr. Gridlock: Apple Maps vs. Google Maps: Which is better for getting around D.C. region?

Google waiting for Apple to move on maps, Schmidt says

Ideas@Innovations: Google takes maps competition underwater (video)