Google Inc. plans to release a version of its desktop search tool for computers running on the Mac operating system from Apple Computer Inc. , Google chief executive Eric Schmidt said on Friday.

Schmidt did not set a timetable for a Mac version of Google Desktop, saying it had to be rebuilt from the ground up because of the fundamental differences between the Mac OS and Windows.

“We intend to do it,” Schmidt said at a University of California-Los Angeles conference commemorating the 35th anniversary of the Internet.

Google released the desktop tool earlier this month, staking out early ground in a battle for personal information retrieval that is expected to eventually include players like Microsoft Corp. and even Apple.