Schmidt has served on the Apple board since August 2006, and both companies make Web browsers and other software. But in July, Google announced it was working on an operating system, which would put Google in more direct competition with Apple. Google also launched the Android mobile operating system project in November 2007.

"Eric has been an excellent Board member for Apple, investing his valuable time, talent, passion and wisdom to help make Apple successful," Steve Jobs, Apple's CEO said in a statement. "Unfortunately, as Google enters more of Apple's core businesses, with Android and now Chrome OS, Eric's effectiveness as an Apple board member will be significantly diminished, since he will have to recuse himself from even larger portions of our meetings due to potential conflicts of interest. Therefore, we have mutually decided that now is the right time for Eric to resign his position on Apple's board."

In late July, Apple rejected Google Voice as an application to run on the popular iPhone. Google Voice is a telephone management system that allows users to share a single number among all their phones. It offers SMS (Short Message Service), voicemail, and speech-to-text conversion of incoming voicemail messages.

On Friday, the U.S. Federal Communications Commission wrote to Apple, AT&T and Google questioning the rejection of Google Voice and related applications from the iPhone App Store.