Google Inc Chief Executive Eric Schmidt is resigning from Apple Inc's board of directors, the companies said, citing increased competition between the two leading technology companies.

The move, which Apple CEO Steve Jobs said was mutually agreed upon, comes amid increased regulatory scrutiny of the relationship between Google, the No. 1 Internet search company in the U.S., and Apple, the maker of iPhones and Mac computers

Jobs said on Monday that with Google's recent introduction of a computer operating system, now is the right time for Schmidt to step down from Apple's board.

Last month, Google revealed plans for software for personal computers based on its Chrome Web browser, which would compete with Microsoft Corp's Windows as well as Apple's OS X system.

At the time, Schmidt said he would talk to Apple about possibly recusing himself from its board. The Google executive has been on Apple's board since 2006.

Unfortunately, as Google enters more of Apple's core businesses, with Android (software for mobile phones) 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 statement.

The U.S. Federal Trade Commission is looking into whether ties between their boards violate antitrust laws. Schmidt and former Genentech CEO Arthur Levinson are directors of both companies.

The move also comes days after the Federal Communications Commission said it is looking into Apple's decision to reject Google's voice application for the iPhone. Google Voice allows users to store transcripts of voicemail messages in their email inbox and find specific information within a phone message.

Both Apple's and Google's shares moved higher in morning Nasdaq trading, with Apple climbing 1.7 percent to $166.10, and Google shares rising 1.6 percent to $450.11.

Microsoft shares also rose, gaining 1 percent to $23.76. The Nasdaq Composite Index was up 0.6 percent.

(Reporting by Franklin Paul, additional reporting by Sinead Carew and John Poirier in Washington, editing by Maureen Bavdek and Derek Caney)