The U.S. Federal Trade Commission said Monday that despite Google Inc. (GOOG) Chief Executive Eric Schmidt's resignation from the board of Apple Inc. (AAPL), it will continue investigating the companies' relationship.

"We have been investigating the Google, Apple interlocking directorates issue for some time and commend them for recognizing that sharing directors raises competitive issues, as Google and Apple increasingly compete with each other," FTC Bureau of Competition Director Richard Feinstein said in a statement.

The commission said it will continue investigating "remaining interlocking directorates" between Google and Apple. The boards share another member: Art Levinson, the former chief executive of Genentech.

Schmidt resigned Monday from the board of Apple due to potential conflicts of interest.

The FTC has been investigating for months whether Schmidt's membership on the Apple board amounts to a violation of antitrust laws.

Schmidt has been an Apple board director since August 2006, and the two companies have partnered on myriad products. Apple, for example, uses Google Maps in its iPhone as its mapping software. Additionally, Google has said it was developing a computer-operating system that would bring it into competition with Apple.

-By Darrell A. Hughes, Dow Jones Newswires; 202-862-6684; darrell.hughes@dowjones.com