The shareholder-led campaign for an overhaul of Rupert Murdoch's News Corporation is gathering momentum, with a call from the advisers Institutional Shareholder Services for 13 of the company's 15 directors to be voted off the board.

ISS, whose 1,700 clients include pension funds, trade union funds and asset managers in the United States and around the world, issued a condemnation of the media conglomerate's executive and independent directors on Monday.

It said the phone hacking scandal had "laid bare a striking lack of stewardship and failure of independence by a board whose inability to set a strong tone-at-the-top about unethical business practices has now resulted in enormous costs – financial, legal, regulatory, reputational and opportunity – for the shareholders the board ostensibly serves."

ISS wants the firm's founder, Rupert Murdoch, and his sons James and Lachlan voted off the board at the shareholder meeting on 21 October.

An executive summary of the ISS advice to shareholders says the problems stretch back to at least 2004, when News Corporation moved its corporate base from Australia to Delaware. It is also advising a vote against the executive compensation plan, complaining that Rupert Murdoch, the chief executive and chairman, received a cash bonus of $12.5m in 2011, up from $4.4m the year before, despite the revelations of the extent of illegal practices at the News of the World this year.

The only directors ISS recommends voting in favour of are Joel Klein and James Breyer, as they have served on the board for just a few months. Klein runs the company's education division, while Breyer is a partner in the venture capital firm Accel and serves on the boards of Walmart and Dell.

ISS said: "Shareholders elect independent directors to protect against governance risk of self-inflicted damage to corporate reputation, viability and long-term shareholder value. The independent directors, rather than embracing their central governance role, opted not to guard the guardians."

The advice follows several calls from proxy advisory firms for a radical News Corp overhaul. Glass Lewis, which advises institutions with more than $15tn in assets, said shareholders should vote against James and Lachlan Murdoch and four other directors.

The UK's Pirc, the Local Authority Pension Fund Forum, which represents £100bn of pension funds, and the Australian Council of Superannuation Investors have also urged voters to oust directors.

News Corp said it "strongly disagrees" with the ISS advice. "The company takes the issues surrounding News of the World seriously and is working hard to resolve them, however ISS's disproportionate focus on these issues is misguided and a disservice to our stockholders."