Google Inc. (GOOG) Chief Executive Eric Schmidt is resigning from Apple Inc.'s (AAPL) board as the two companies' businesses increasingly overlap and the U.S. government investigates the close ties between the two boards.

The two technology giants are fighting on more battlefields as Google, over the past year, has released an operating system for smartphones called Android, a new Web browser called Chrome and plans to release its own operating system for computers, known as Chrome OS.

Meanwhile, the U.S. Federal Trade Commission late Monday said it would continue investigating the companies' "interlocking directorates," which is now down to Genentech Chairman Arthur Levinson. Genentech officials declined to comment.

Apple CEO Steve Jobs, who called Schmidt "an excellent board member" since he took the post in August 2006, said Monday that both sides agreed now is the right time.

"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," Jobs said in a press release.

Many analysts had expected Schmidt would eventually be compelled to leave Apple's board.

"Over time, the two companies are going to be butting heads - Google is pushing Android and that clearly competes with the iPhone operating system - so it kind of makes sense for them to go their separate ways," said Jefferies & Co. analyst Youssef Squali.

It was not clear who would replace Schmidt on Apple's board, and Apple officials were unavailable for further comment. Apple's board has historically seen very little turnover. The last time a board member resigned from Apple was two years ago when Chief Financial Officer Fred Anderson left after an independent investigation into its stock option grants.

Apple's shares rose 1.9% to $166.43, while Google's gained 2.1% to $452.21.

Schmidt has recused himself from Apple meetings when the board discussed Apple's iPhone, which accounted for about 18% of its $8.1 billion in fiscal second-quarter revenue. With Google's planned operating system, Schmidt may have had to excuse himself when the board discussed Macintosh computers and software.

With competition between the two tech giants growing, Endpoint Technologies analyst Roger Kay said Apple would likely have increasing issues with Schmidt "having access to the inner sanctum."

"The overlap of the two companies' businesses has increased to the point where Schmidt has become ineffective as an Apple director," Kay said.

Although the issue has grabbed headlines, it hasn't shaken analysts and investors. Apple shares have risen nearly 144% since August 2006.

Apple and Google have partnered on myriad products. Apple, for example, uses Google Maps in its iPhone as its mapping software.

Still, there are also signs that the relationship may have become more contentious. For example, last week, Apple rejected Google's application to distribute its Internet telephony software, Google Voice, through Apple's App Store, raising further issues with regulators.

The Federal Communications Commission launched an inquiry into Apple's rejection of the application, seeking information on how AT&T Inc. (T), the iPhone's exclusive carrier, was consulted in the decision, if at all.

In October, Google launched the Android mobile operating system as well as the Android Market, which is similar to the iPhone's App Store and lets users download various applications such as games and social networking services. Though the number of Android device users is still a fraction of Apple's more than 25 million iPhone users, many device makers have plans to use Android in upcoming devices, and analysts believe it could become a stronger competitor to Apple.

More recently, Google announced plans to launch new software to power lightweight computers that run online applications. Google has downplayed the degree to which the software, known as Chrome OS, competes with traditional operating systems made by Apple and Microsoft Corp. (MSFT).

-By Jerry A. DiColo, Dow Jones Newswires; 212-416-2155; jerry.dicolo@dowjones.com

(Jessica E. Vascellaro and Yukari Iwatani Kane contributed to this report.)