The group, led by Amalgamated Bank and several municipal and union pension funds, yesterday filed an amended lawsuit alleging "egregious" behaviour and failed corporate governance at News Corp amid the phone hacking scandal.
The legal action was initially launched in March over Murdoch's $675 million (£415m) deal to buy his daughter Elisabeth's Shine Group, amid claims that it was a case of "rampant nepotism".
Murdoch has now been accused of using News Corp's resources for "his own personal and political objectives", while the group also claim that it was "inconceivable" his son James would not have been aware of widespread phone hacking at the News of the World.
In a legal filing in Delaware, where News Corp is registered, the group said: "It is inconceivable that [James] Murdoch and his fellow board members [at News International] would not have been aware of the illicit news-gathering practices.
"And yet, the board took no real action to investigate the allegations until July 7, 2011, when Murdoch selected two of his co-directors to deal with the imbroglio.
"These revelations should not have taken years to uncover and stop. [They] show a culture run amuck within News Corp and a board that provides no effective review or oversight."
The shareholders also noted that News International chief executive Rebekah Brooks, a former editor of the News of the World, was "consistently promoted even while the scandal was unfolding".
"The fact that the board has been so passive despite years of misconduct is a testament to how lacking in independence its members are from the Murdoch family, shareholders allege. This has led to a 'Murdoch discount' in the marketplace," the complaint adds.
The group is seeking to block News Corp from adding Elisabeth Murdoch to the company's board and "to put an end to Rupert Murdoch's use of company assets to serve personal and family agendas, without regard for public shareholders".
Jay Eisenhofer, the co-managing director of Grant & Eisenhofer and co-lead counsel to shareholders, said: "News Corp's behaviour has become an egregious collection of nepotism and corporate governance failures, with a board completely unwilling to provide even the slightest level of adult supervision.
"The result has been a piling on of questionable deals, a waste of corporate resources, a starring role in a blockbuster scandal, and a gigantic public relations disaster. It is way past time that the News Corp board step in and initiate serious changes to the company's corporate governance."
Last night, a new poll indicated that 82% of the British public want to see Brooks step down after the torrent of shocking phone hacking allegations against the News of the world.