Another major investor has joined calls for the Murdoch family to step down from the helm of media empire News Corp following a phone hacking scandal, according to a British newspaper.

The Sunday Telegraph said the California State Teachers' Retirement System (CalSTRS) had added its voice to opposition already aired by shareholders including the California Public Employees' Retirement System (Calpers) and Hermes Equity Ownership Services.

Given the lack of independent directors, effective board leadership is even more important to provide proper oversight to the company and management, the newspaper quoted CalSTRS as saying, adding it wanted the whole News Corp board replaced, including Rupert Murdoch and his sons James and Lachlan.

The Sunday Telegraph said CalSTRS owns more than 6 million News Corp shares.

CalSTRS could not immediately be reached for comment.

The criticism from top investors sets up what is likely to be a turbulent annual shareholder meeting for News Corp and the Murdochs on October 21.

The company is battling to recover from a phone hacking scandal which led to the closure of its British weekly newspaper News of the World in July.

Rupert Murdoch controls News Corp through a 40 percent stake in its voting stock.

Last week, corporate governance watchdog ISS called for the Murdochs and 10 other directors to step down. News Corp said it strongly disagreed with its analysis.

(Reporting by Mark Potter; Editing by Sophie Walker)