WASHINGTON (Reuters) - The U.S. Federal Trade Commission said it will continue to investigate the relationship between the boards of Apple Inc and Google Inc, after Google’s chief quit Apple’s board on Monday.

Google CEO Eric Schmidt talks to a reporter at the Sun Valley Inn in Sun Valley, Idaho July 9, 2009. REUTERS/Rick Wilking

Richard Feinstein, director of the FTC’s bureau of competition, commended both companies for recognizing that sharing directors raises competitive issues, in light of the resignation of Google Chief Executive Eric Schmidt from Apple’s board.

Feinstein said regulators have been investigating the Google-Apple tie for “some time,” even as the two companies increasingly compete with each other in markets such as smartphones and operating systems.

“We will continue to investigate remaining interlocking directorates between the companies,” Feinstein said.

Antitrust experts say, typically, a resignation like Schmidt’s would have closed the FTC investigation. But because one other person still sat on the boards of both companies, the agency was not likely to close its investigation down yet.

Former Genentech CEO Arthur Levinson remains a director of both companies.

“Generally it would have shut down the investigation because they (regulators) achieved what they wanted to achieve,” said Gary Reback at the law firm of Carr & Ferrell.

A consumer rights group criticized Schmidt for taking too long to leave Apple’s board and called on Levinson to choose either Apple or Google.

“Nonetheless, we’re glad Schmidt finally did the right thing,” Consumer Watchdog said in a statement. “We call on Levinson to act responsibly and choose one company or the other.”

David Turetsky, a former deputy assistant attorney general for antitrust under the Clinton administration, said Levinson’s dual position could be why the FTC is leaving the probe open.

“As the convergence of their two businesses happens, it is no doubt hard to have overlapping directors,” said Turetsky, co-chair of the antitrust practice at Dewey & LeBoeuf.

“Schmidt did the right thing.”

Experts said an end to the FTC investigation would have done little to reduce the regulatory spotlight on Google in Washington mainly because of the company’s market share.

Google, the No. 1 Internet search engine and provider of text-based search ads, has been praised for being a successful American company, but that success comes with increasing scrutiny from regulators.

In another investigation, the Justice Department is looking at Google’s settlement with the Authors Guild and Association of American Publishers that would allow it to create a massive, online digital library.

“Google is in the sights of regulators,” said a former FTC antitrust attorney under the Clinton administration, who declined to be named. “This is just the first of many instances where they are going to encounter regulatory scrutiny.”

Last Friday, the Federal Communications Commission sent letters to Apple, Google and AT&T Inc seeking information about why Apple rejected Google’s voice application for the iPhone.

AT&T is the exclusive carrier for the Apple’s popular iPhone in the United States.

“Asking questions can’t hurt,” FCC Commissioner Robert McDowell said in an interview with Reuters on Monday. “Responses to the letters could be helpful.”

The FCC’s inquiries come at a time when its chairman, Julius Genachowski, is looking into the ability of consumers to choose their mobile handsets and how these arrangements also affect competition and innovation.