In an open letter to Fairfax chairman Roger Corbett, the company's largest shareholder, Gina Rinehart, has called on him to resign should the media company's share price not reach 87 cents before the company's annual general meeting in November.

Rinehart, who owns 18.7% of Fairfax, wrote that should the stock reach 87 cents, it would be trading at only a 50% discount since Corbett took office in October 2009.

Fairfax stock is currently trading at 56 cents.

"To limit the loss under your chairmanship to only 50% is not an unreasonable expectation, although perhaps shareholders would prefer a higher target?"

Rinehart also claims the "disagreements" between her and Corbett do not revolve around the charter of editorial independence. "I don't recall you even sending me that charter, and very little time or correspondence was spent on discussing it," she wrote.

In a statement released shortly after, Fairfax denied Rinehart's claims. It said the board's decision to not grant Rinehart a board seat did revolve around the charter.

"Mrs Rinehart's letter today has once and for all unmasked her motives for her continual attacks on the company and its board," the statement read.

It also compared Fairfax's share price decline to those of its competitors, arguing that the fall was comparable to what had happened to other media companies over the period of Corbett's chairmanship.

Rinehart's full letter to Corbett can be read here, and Fairfax's response is here.