Last week, investor group Firebrand Partners and hedge fund Harbinger Capital Partners doubled their stake to 10%. They have now increased it again to 15.6% and are pushing for four board seats.
Scott Galloway, the Firebrand Partners founder, has called on the New York Times to invest more heavily in its digital operations.
The New York Times named Dawn Lepore, CEO of online pharmacy Drugstore.com, as one of its board nominees last week, but this did not to placate Firebrand and HCP.
The New York Times said it was looking at the slate of board nominees put forward by the investors, which includes Galloway, but has asked shareholders to back its own proposed slate of directors.
According to the New York Times newspaper, the media firm, which also owns the Boston Globe and the International Herald Tribune, is open to "striking a deal with its new investors and altering that slate ahead of the April 22 annual meeting".
Catherine Mathis, a New York Times Company spokeswoman, said: "The Harbinger nominees are still under review."
This was not well received by Firebrand and HCP, which voiced strong disappointment in a statement of its own: "As the company's largest shareholder, with more than 15% of the Class A shares, we are particularly concerned that the company refused to interview any of our nominees despite our repeated offers to meet at their convenience."
However, while the investors are the largest shareholders with 15.6% of Class A stock, family chairman, Arthur Sulzberger Jr., holds more than 80% percent of the Class B voting stock -- these shares are not publicly traded and can be used to select nine of the 13 board seats.
Class A shares have to battle it out for the remaining four minority seats, which the Sulzberger family still has some sway over.
The battle for Class A stock has sent the New York Times' share price firing upwards, leaping from $15 in January to a high of more than $21 earlier this week, before falling back to $19.69 yesterday.
The media company also last week nominated former CEO of Salomon Inc Robert Denham as one of its nominees alongside Lepore.