Walt Disney Co. defended its executive structure and pay yesterday after a shareholder governance group criticized Chief Executive Bob Iger’s compensation and his added role as chairman.

Disney, in filings with securities regulators, said a report by Institutional Shareholder Services was “deeply flawed and out of touch with shareholder interests.”

The entertainment and theme-park company said in October that Iger would remain CEO through March 2015 and take on the additional role of chairman at the company’s annual meeting this month.

ISS, in its report, said Disney had “reversed an earlier commitment to independent board leadership without transparency or shareholder input.”

The group said the company’s move was “an about-face” from reforms adopted after shareholders objected in 2004 to former CEO Michael Eisner also holding the chairman’s job. Disney said it made no such commitment.

ISS said Iger’s pay “has risen sharply over the past five years despite lackluster shareholder returns.”

Disney countered that the company had delivered “exceptional total shareholder return” during Iger’s six years in the company’s top job starting in October 2005. Disney said Iger’s pay was in line with that of media industry peers.

His total compensation rose 13 percent in fiscal 2011 to $33.4 million.

Shares of Disney rose about 57 percent from Oct. 1, 2005, through the end of 2011.