TOKYO (Reuters) - Google Inc has made no move to provide Google Maps for the iPhone 5 after Apple Inc dropped the application in favor of a home-grown but controversial alternative, Google's Executive Chairman Eric Schmidt said.

Apple launched its own mapping service earlier this month when it began providing the highly anticipated update to its mobile software platform iOS 6 and started selling the iPhone 5.

But users have complained that Apple's new map service, based on Dutch navigation equipment and digital map maker TomTom NV's data, contains glaring geographical errors and lacks features that made Google Maps so popular.

"We think it would have been better if they had kept ours. But what do I know?" Schmidt told a small group of reporters in Tokyo. "What were we going to do, force them not to change their mind? It's their call."

Schmidt said Google and Apple were in constant communication "at all kinds of levels." But he said any decision on whether Google Maps would be accepted as an application in the Apple App Store would have to be made by Apple.

"We have not done anything yet," he said.

Google and Apple were close partners with the original iPhone in 2007 and its inclusion of YouTube and Google Maps. But the ties between the two have been strained by the rise of Google's Android mobile operating system, now the world's leading platform for smartphones.

Schmidt said he hoped Google would remain Apple's search partner on the iPhone but said that question was up to Apple.

"I'm not doing any predictions. We want them to be our partner. We welcome that. I'm not going to speculate at all what they're going to do. They can answer that question as they see fit," he said.

Google provides Android free of charge and allows developers to add applications on an open basis, betting that by cultivating a bigger pool of users - now at over 500 million globally - it can make more money by providing search functions and selling advertising.

"Apple is the exception, and the Android system is the common model, which is why our market share is so much higher," Schmidt said, adding that success was often ignored by the media, which he said was "obsessed with Apple's marketing events and Apple's branding."

"That's great for Apple but the numbers are on our side," he said.

At one point, Schmidt, who was in Japan to announce the launch of Google's Nexus tablet here, used the device to show off a new function of Google Maps.

The feature allows users to shift their view of an area by moving the device in the air without touching the screen, similar to the effect of looking around.

"Take that Apple," he said, adding quickly, "That was a joke by the way."